An energy and determinist approach of quantum mechanics
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- Elisabeth Dalton
- 5 years ago
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1 A s quu s P VAUDON X Uvs Ls - F 5
2 T s Fs ss DIRA qu s sus Iu... 4 DIRA qu... 9 DIRA -ss... 6 ½... v DIRA qu... E DIRA qu s sus s s s... 7 E sus DIRA ss T wv- u T us DIRA () P DE BROGLIE wv G DIRA qu... 7 T us DIRA ()... 8 us s... 8 T E DIRA qu s sus s s DIRA qu s s KLEIN-GORDON qu s s... 9 E sus DIRA qu s s E sus DIRA qu s Y - Y O sus... 6 ss sus s s... DIRA us... 7 G DIRA qu s s... us... 7 Fu s T DIRA qu v : ss... 4 E sus D qu v s s... 4 Es s... 47
3 G us... 5 B... 54
4 Fs ss D qu s sus
5 I Iu Ts us ss s s s s quu s s sus s u. T s s v su s s u s DIRA qu. As s s s s usu sss, u ss s us. T w s v sv w sus s s DIRA qu. A u s, s w ss. I s u s vs sv su, w ss s s s, wu sv vu. Ts w s s suu: s v wv,. U u s, s u svs ss s vw. I sus w, u s ss v ss u sv s w us w su u s. T v ws s u wv- u, w us v s w, w w s ss, w s vs s ss. Ts v s w vs w s wv s usu ss. T w s s u s s s, u w sus s, DIRA qu. Ts sus, s, ss w s u u s qu. I, u, s s s, wv- u. I - A I ss wv qus, s qu ss u wv s usu s s. O us s s s, v s s: 4
6 A. A...J (I-)... (I-) I wv qu ö K-G, su ψ u s qu wu s ss, us s s s qu: ( ) ( ) E (I-) ( ) ( ) (I-4) Ts s ψ su s u wv. T s qu s ss s ss. T u ψ s, u w s vw quu s, v v qu ψψ vu s, vv vu w s w : v (I-5) V I w s vs, s s. T s qu ss s, ss w s vs suss v qu ψψ vu s. T s s ss vu V w s us v E : v E (I-6) V Wv us ssu s s squ E. T wv u ψ s us w squ. A s v s, u s u w w s sus D qu s sv s s v s. I - T s I s v, u-vs s v s qus. I ws su- s s s s w s vu. 5
7 6 F ss v s v, u-v u- s ss s ws: E E v v v E P ~ (I-7) I s ss, E s w ss, v w s v, s ss s: v (I-8) T su- s squ u-v us s w: E (I-9) : E² - ²² = (I-) w s us u: v (I-) O s s w, w s ss, ss s s qu : v E (I-) w s s ss. W u vu s:
8 E (I-) v v v ss sv s v: E (I-4) W s su ss v, w ss v s v, s s : - A sv w E, w w w susqu us s wv - A s us : - A s ss s: L us s ssu, w s, s s s, s w s s, s. I - s s, w s us. O s ssu s ss s s. Ts s s, w s. s us, s u s, s s wv, s qu ss. W s u w w w s ss wvs. Ts s s sss wv s. I w ssu ss wu ss, w u wv s ss, s sv. T s s v ss s s w s, u ss s s u s w s s quu. I s, wvs u w s, us w s v s. I s, s w. I w w u su s s wv ss, w su s w s s w. Ts ssu ss v u wv. I s v, s w s us. W su s w s w w vus s s, u w vs qu sv (I-4). 7
9 L s u, w w w w w s s: sw s qus s w us. Bu w w sw w ssu s s s, s quu ss s ss w u s. 8
10 II DIRA qu T DIRA qu s s u qus ss. I ws w w v qus quu s: HRÖDINGER qu KLEIN-GORDON qu. I s su w us ss w s sv. T v s s s s suss u s qu quu ss w s wss s su w w w u. I's us, s, DIRA qu, u s us s s su. I - T HRÖDINGER qu A s (,,, ) w s s v ss s s ws s wv qu: (,,, ) (,,, ) (II-) v W w s w sus v, w u: (,,, ) (,,)( ) (II-) wv qu qu s: (,,) (,,) (II-) v Fw Lus D BROGLIE ssu ss ss v v v wv wv = /v, w s PLANK s, - wv qu s: (,, ) (,, ) (,, ) (,, ) (II-4) v O, ss s, E s s su s E s E, w ws w: 9
11 E v E E (II-5) w s u sussv: E v E (II-6) (II-7) v E E Ts s s u wv qu (I-4) vs - HRÖDINGER qu: (,,) E E (,, ) w (II-8) T us s s s s u. F, wv w ws, w w wv u u :, w ² = - (II-9) I quu w w = /v w w E s qu wv : E (II-) w susu:, E w v (II-) I v s ss v, ws:, E E E, (II-) s s ss (II-):,, (II-) F s (II-) (II-), u qu us ss vs s qus w w s qus quu :
12 E (II-4) (II-5) F ws s v ss s su : E E E v E E (II-6) I s u u wv u : E E (II-7) us us qu (II-4) (II-5): ( ) ( ) E ( ) E (II-8) w s HRÖDINGER qu. Ts qu ws ss s ss s s w s s s BOHR, u s u w s s su su s suu vs u s. II - T KLEIN-GORDON qu T qus HRÖDINGER qu u qu us v us ss s. Rv us s ws s s u us s v u LORENTZ s: E 4 (II-9) w us qu (II-4) (II-5): 4 ( ) ( ) (II-) w s KLEIN-GORDON qu. W s wv qu w s : ( ) ( ) (II-)
13 A vw s sus ws sw s qus, u s s s w s / s w s s vs. III - T DIRA qu B w vs sv qu: 4 E (II-) us qu quu s: E (II-) I ss KLEIN-GORDON qu u: 4 (II-4) A s s DIRA, w v s su v qu s v s qu s squ: (II-5) I s v s u s s, su sv qu v squs: (II-6) I s ss ss s (II-5) (II-6), u u s w w, ss su s s qu (II-4) qu (II-5): (II-7) (II-8) Ts s uqu, u s s s D:
14 (II-9) T w PAULI s : (II-) s : (II-) T suu s qus s su u v: (II-) I u ss qus s su s ss s w, w u qu (II-6) α. I s w s squ s qu : (II-) W u : (II-4) w s vvs: (II-5) T, w s u. T s γ s ws:
15 4 (II-6) (II-7) (II-8) (II-9) T s s ss ss PAULI s: (II-4) w w :, (II-4) s w qu wv qu ss v w 4 u, w ss s v :
16 5 (II-4), s, u vvs qus ss 4 qus, u : () () () () (II-4) Ts qus sw 4 qu ss w wv, wu s ss s s u. T s s ss vs us w w s u vs, u s s s, s s s u v uss.
17 III DIRA -ss I vus, w u sus D qu s qu w 4 s: A u vw ss D: (III-) () () () () (III-) sws s sus u v w s. T s s s, s u u ss s : () () () () (III-) T, w u: 6
18 7 w (III-4) D ss s w w u sss: () (III-5) () (III-6) w sw qus φ χ s v s s w s ss. A w s s M : M (III-7) T u ss (III-5, 6) s ss s : M () M () (III-8) s: M M () (III-9) I s ssus, s ss w w ss-ss w w ss. O, w s s sus w (- ω) w E, E.
19 I s w s s w s s wv s(). Is s suss I, w w s. A u v s (III-9), u ss ss s : E M M (III-) u : E M M (III-) A us w su v s u η s (III-) s s ² s (III-). T us ws w s s, s ss ss, s ss w. I - s v I s ss sw sus w sv s s ss, v sus s s -s ss. T sw s, w s s:,, s, vvs w s,,, M s. W v (III-): E (III-) s: E E (III-) W ss w s φ s qu s ss, w ss w s χ s qu s s, us ss ss w -. W u s φ s ss w, w s χ s ss w. T su D qu, w us w ss suus, ws s v s. I v, s φ s ss w : 8
20 9 (III-4) w w ss ss w ss s s. T s s s ss w s s s «u» ( ), s s ss w s s s «w» ( ). As w v, w w s: (III-5) w s ss s v. G s sus, w s u s ss DIRA ss w s s: P sv s "u". "P sv s "w". P w v s "u". P w v s "w". II - s W s v, M s u, w us s (III-) :
21 E M M (III-6) Ts s sws w ss. As ss squ, w w, v wu s ss w s v. I s, v s (III-6): E E M M (III-7) s E M E M s: E E M M (III-8) (III-9) Ts ss s s w w, s s E s w 4 s D ss v, w ss, w u. I s ss v v s s (III-9) v. W us M s ss PAULI s : I vs: (III-) M (III-) W u susu vvs (III-), us quu s, ws s :
22 ˆ ˆ ˆ (III-) Ts ws s M : ˆ ˆ ˆ M (III-) I ws us w wu v sws s: W : (III-4) "v" PAULI s, : (III-5) "v" w ss us quu s. T ss M (III-) u w s, us usu s s u w w vs: M. (III-6) W u s w w sss s w w ss w su su DIRA, v E : E. E. (III-7)
23 B susu s, s s, w :... ( ) E E E (III-8) Us PAULI s ws squ vs, s : E ( ) (III-9) Ts s w : E (III-) : E (III-) Ts s s ss sus ss w vs sv, u s w ss sus w v s : E (III-)
24 IV ½ T su s ss vus suss s w s ss, wu w s w. W w us s s, u w su ss DIRA. I - T u u F ss, M, v u O, u w s L s ss s us u: L OM OMv (IV-) I s v qu w s u s. I s,,, s s v,,, s u v: OM (IV-) w s u u : L L L (IV-) T s quu s ss vs "s"' qus "qu " w s "s" "qu ", w ws s u u : Lˆ Lˆ Lˆ ŷˆ ẑˆ ˆˆ ẑˆ ˆˆ ŷˆ (IV-4)
25 w s us u, wv u ψ s s w: ˆ ˆ ˆ ŷ ˆ ẑ (IV-5) T s v u u ws wu u u ss w vvs u, u s s sss s u u s. Ts s v w s w w w w ss s s u s. T v s u, ws ss w vv s u s, s su s. Ts s su u sw ws w v w quu s: I A B w s, sw A B s : A,B AB BA (IV-6) F, w sw s s s wv u sw, w s s s w s sw s -:, (IV-7) I w u sws u u s (IV-4), v w : Lˆ,Lˆ Lˆ Lˆ Lˆ Lˆ Lˆ Lˆ,Lˆ Lˆ Lˆ Lˆ Lˆ Lˆ Lˆ,Lˆ Lˆ Lˆ Lˆ Lˆ Lˆ (IV-8) T s s u u s (IV-4). O s (IV - 8) s sussv: Lˆ ( ) Lˆ ( ) (IV-9) Lˆ Lˆ ( ) (IV-) 4
26 Lˆ Lˆ ( ) (IV-) vs s: Lˆ Lˆ ( ) (IV-) Lˆ Lˆ ( ) (IV-) Lˆ B su (IV-) (IV-), s su s (IV-8): Lˆ ( ) Lˆ Lˆ ( ) Lˆ (IV-4) T (IV-8) s s u s. Ev su w, s sw u ss qus uws w ss s uw s s s s (IV-4) u u quu s. II - T s u u T s vus s us ss u u wv u ψ. Ts s ss u : Lˆ,Lˆ Lˆ Lˆ Lˆ Lˆ Lˆ Lˆ,Lˆ Lˆ Lˆ Lˆ Lˆ Lˆ Lˆ,Lˆ Lˆ Lˆ Lˆ Lˆ Lˆ (IV-5) us ssu u DIRA ss, s s w wv us. I vus, w sw su sv ws s s: (IV-6) T qus ss s: w w (IV-5) ss u u wv u, u u s s u w wv us? I ws, s su, w w w: 5
27 6 Ŝ Ŝ Ŝ Ŝ Ŝ,Ŝ Ŝ Ŝ Ŝ Ŝ Ŝ Ŝ,Ŝ Ŝ Ŝ Ŝ Ŝ Ŝ Ŝ,Ŝ Ŝ (IV-7) s: Ŝ Ŝ Ŝ Ŝ Ŝ,Ŝ Ŝ Ŝ Ŝ Ŝ Ŝ Ŝ,Ŝ Ŝ Ŝ Ŝ Ŝ Ŝ Ŝ,Ŝ Ŝ (IV-8) I s s Ŝ,,Ŝ Ŝ s s s us s wv u: us X s s s us s s u u s: Ŝ Ŝ Ŝ Ŝ Ŝ,Ŝ Ŝ Ŝ Ŝ Ŝ Ŝ Ŝ,Ŝ Ŝ Ŝ Ŝ Ŝ Ŝ Ŝ,Ŝ Ŝ (IV-9) T PAULI s, w, s s : (IV- ) B u qu ħ, s sw (IV-9) s w:,,, (IV-) s:, (IV-)
28 W s sw ss (IV - 9), s s w s. I w w s s s u u, w us ss u ½ PAULI s. I s s w u s ½. s ws: I su, s Ŝ,Ŝ, Ŝ su, w vs (IV-9), Ŝ Ŝ Ŝ (IV-) I w v w v s s s u u, w w s s s. T ss, w ss vus, s (IV-) (IV-4), s ss w s (IV-) v s, w s (IV-4) v us su s. T ss v ss v s, s w s s u u s us ss s. III - T u u s T s s ws s. W w us s sw w ss s ss s w us s s, u s u u. T s s, us s ss ss -s s, u s wv u ψ s, s φ w w s s. W us s ss θ Eu s, ws s s s w O. Ts O, w s w w w s M M w s M(,) M'(','). 7
29 M (, ) θ φ M(,) O φ Fu (IV-): R O T s w s (,) (',') ss s ws: =.s (φ) =.s (φ) (IV - 4) ' =.s(φ') =.s (θ + φ) = (s (θ) s (φ) - s (θ) s (φ)) =.s (θ) -.s (θ) ' =.s(φ') =.s (θ + φ) =. (s (θ) s (φ) + s (θ) s (φ)) =.s (θ) +.s (θ) (IV-5) s w w ss: ' s ' s ' s s (IV-6) F s - θ, s s sus: ' s ' s ' s s (IV-7) I s v u, w ss u s, s s quv. F θ, v s s s us u w u - θ. T u s s, w s w s u ψ, w w w O s θ wv u ψ: 8
30 Rˆ, (,,) (',',') (IV-8) I s s, w vus s, w us s s (IV-). T s s ss w s, u u Lˆ (Lˆ, Lˆ, Lˆ ) w ws us v (IV-4), s s (IV-) ss s. Ts w s, s. (IV-8) v v: Rˆ, (,,) (.s.s,.s.s,) (IV-9) u vs s s (θ) s (θ) s s δθ: Rˆ, (,,) (..,.,) (IV-) M us v s u w vs w v s u sv qu ε η: (,) (,) (, ) (,) (IV-) s (IV-) s : Rˆ, (,,) (,,) (IV-) I s us s "s" "us" w: ˆ ˆ ˆ ŷ ˆ ẑ (IV-) v w ss: Rˆ, (,,) (,,) ˆˆ ŷˆ (,,) (IV-4) W u u (IV-4): Lˆ ˆˆ ŷˆ (IV-5) W u ss s u O s θ, wv u ψ, u u : 9
31 Rˆ, (,,) (,,) Lˆ (,,) Î Lˆ (,,) (IV-6) w Î s. Rˆ W w u s ss s : Î Lˆ, (IV-7) Ts s θ, sv ws. O ss s v s N, w s ws : w ss s δθ s (IV-7) w θ/n. Rˆ, N Î N Lˆ (IV-8) O ws θ, w us N s s θ/n: Rˆ, Rˆ, N N Î N Lˆ N (IV-9) A w w w s : Rˆ, Rˆ N, N N Î N N Lˆ N (IV-4) Us w su: N N N () (IV-4) w ss s O θ, u u Lˆ : Rˆ Lˆ, (IV-4) I s u s, s ss w us wvs w ss.
32 I s sw v Lˆ Lˆ,Lˆ, Lˆ Ŝ,Ŝ, Ŝ su Ŝ w-s s, s s PAULI s w s (IV-) : Ŝ Ŝ Ŝ (IV-4) T s O θ, s, s w : Rˆ Ŝ, (IV-44) s: Rˆ, (IV-45) F vw, w u X ws s w. W vss su us v ss u. F M, s vs: (M) M! M M! M!... (IV-46) Hwv, s ss u s O, O, O. O u O s: T s, w ws v : Rˆ, s s s s (IV-47) O u O s:
33 Rˆ, Ŝ (IV-48) T u s X ws sw ss s vs v ss s s us s M su w s: s() s() A ( A) (IV-49) s() s() Ys ss u O s: s s Rˆ, (IV-5) s s O u O s: Rˆ, Ŝ (IV-5) As vus, u s X ws sw ss s v us s s ss s s M su w s: s() s() A ( A) (IV-5) s() s() Ys ss u O s: s s s Rˆ, (IV-5) s s s
34 V v DIRA qu T DIRA qu w w ss ss qus s : (V-) () B : =, =, =, = (V-) w s w (V-) us su v s u: μ =,,, (V-) I us u s qu s v, s s s s s w s s v s v. T s, us, u s. T v ws ss s s v s w. I su s ws: L us s w DIRA qu s w (V-) v. I w, w u s s μ s s w ' μ ; s w u wv u ψ w w ψ'. T v ws ss qus DIRA qu s w (R'), u : ' ' ' (V-4) A v w ss s w sv. I sss w s qu vvs s, sv s qu s ss us u v qu. O s-w s s sv s u-v u s (ρ,,, ) u :
35 4 (V-5) I s ss sw s qu sus DIRA qu, s qu s u DIRA s (V-5) v. I w J s qu, s w u-v qu s s ws: J J (V-6) A w -v us uss w sw DIRA qu w s: (V-7) w: T,,,,,, (V-8) F (V-6) (V-7), w u u-v u DIRA: J (V-9) w γ μ s s DIRA u II. W v sss s u-v J μ s s DIRA s us: :,,,,,, J (V-) J (V-) :
36 5,,,,,, J (V-) J (V-) :,,,,,, J (V-4) J (V-5) :,,,,,, J (V-6) J (V-7) H su: J J J (V-8) J T J μ s s us s.
37 E D qu s sus s s 6
38 VI s I, ss ss sus DIRA qus u wvs : (,,,) A (VI-) Ts s s s wv w s u qu ω wv v. I s s s su s s s v. I s s su qus u u w s s s w s usu s wvs. W u v s s su w v sus, u sus (VI-) DIRA ss v u, w s s ss v. W v s s sus DIRA ss : () () () () (VI-) w s wv u w s s s w s -s v: 7
39 8 (VI-) I s, w v s us: = s ( ) = s ( ) = s ( ) = s ( ) (VI-4) = s ( ) = s ( ) = s ( ) = s ( ) (VI-5) T wv v s s s,, s, w us ss w v, u s ss., w ws w u-vs: 4-v s: 4-v wv: (VI-6) s,,,,,,,,,,,,,, =,,,, ss w s w sv s uw s wv us,,, sus DIRA ss. Ts s, qu DIRA ss, ss vvs wv us,,, u us ss 6 qus s,,,,,,,,,,,,,. T ss w us ss 64 qus w 64 uws. us us u wu us. T s w s w w v u = ω/.
40 9 Fs qu DIRA ss: () () (VI-7) W u us ss ss w s qu DIRA ss: (VI-8)
41 4 qu DIRA ss: () () (VI-9) W u us ss ss w s qu DIRA ss: (VI-)
42 4 T qu DIRA ss: () () (VI-) W u us ss ss w qu DIRA ss: (VI-)
43 4 Fu qu DIRA ss: () () (VI-) W u us ss ss w u qu DIRA ss: (VI-4)
44 4 T ss 64 qus s,,,,,,,,,,,,,. =,,, w su us: (VI-5)
45 I s us ss ws - su s s. Bu ss ss 64 qus w 64 uws s v. Hwv, s s ss. I s s w,,, η w ws sus s ss, s s us ss sv. I ws u su- us u-v: ~ P E (VI-6) s w s ss s sw s ss s us ss s sv : E (VI-7) T u (VI-6) u-v quu s s u u-v wv PLANK's s: ~ PQ (VI-8) F s ss s, su- s u-v s s s s s ss s ss v ². W u: (VI-9), us us ss DIRA ss (V-): (VI-) (VI-) I su, DIRA ss s sus, s us ss ss w qu sv (VI-). 44
46 I s w ss sw su s s s su KLEIN-GORDON qu w: ( ) ( ) (VI-) s wv u s v -s s ss (VI-), s:,,, ) As( ) s( ) s( ) s( ) (VI-) ( B susu u ψ (VI-) (VI-), w : (VI-4) w suss DIRA ss s sus s s v qu sv (VI-) s ss. Bs s ssus, sw ss 64 qus 64 uws s : (VI-5) I s u v w s s, s, w sv qu s v, sus DIRA ss s wvs. 45
47 VII E sus DIRA ss T vus s w sw w s sus s ss. T v, w us. A ss ss sws w s, s, w w us: (VII-) ss s, ws. T u s sv, w s sus v u ss vus s: (VII-) I - us w s s ss T s ( VII-) ws v s su.φ u s s χ su DIRA ss. I sw s sus, s φ s s ψ sussv w ss s w ψ=, s ψ sussv ss s w w ψ=. 46
48 ψ L ψ L.K.K -.L.η.K.K.K -..K.K -..η.k -.η.k.k.k -..η.k.k.k..k.k -..η.k.η.k.k.k -..η.k -..K.K -.K.K -.η.k..η.k.k.k -..η.k..k.k -.K.K.η.K..η.K -.K.K..η.K.K.K -..K.K -..η.k -.η.k -.K.K..η.K.K.K..K.K -..η.k L.η.K -.K.K..η.K -..K.K -.K.K -.η.k.l.η.k -.K.K..η.K..K.K -.K.K.η.K..η.K -..η.k -L.K.K -..η.k -.η.k -.K.K..K.K -..η.k -.K.K -..η.k.η.k -.K.K -..K.K -..η.k -.K.K -.η.k..η.k..k.k.k.k -..η.k -.K.K.η.K..η.K -..K.K.K.K..η.K.K.K -..η.k -.η.k -.K.K..K.K..η.K.K.K -..η.k.η.k -.K.K -.L.K.K..η.K.K.K -.η.k..η.k..k.k L.K.K..η.K.K.K.η.K..η.K -..K.K.K.K ψ(η²-²).k.k..k.k -..η.k.η.k -.K.K.L.η.K.K.K -..K.K -..η.k -.η.k -.K.K..η.K..K.K -.K.K.η.K..η.K -.K.K..η.K -..K.K -.K.K -.η.k..η.k -.K.K..η.K.K.K..K.K -..η.k.η.k.k.k -..η.k.k.k -..K.K -..η.k -L.η.K.K.K -..η.k..k.k -.K.K.η.K.L.η.K.K.K -..η.k -..K.K -.K.K -.η.k..η.k.k.k -..η.k -..η.k.η.k -.K.K -..K.K..η.K L.K.K -..η.k -.η.k -.K.K..K.K..η.K.K.K.η.K..η.K -..K.K.K.K..η.K.K.K -.η.k..η.k..k.k.k.k..η.k.k.k -..η.k.η.k -.K.K -..K.K -..η.k -.K.K -..η.k -.η.k -.K.K.L.K.K -..η.k -.K.K.η.K..η.K -..K.K L.K.K -..η.k -.K.K -.η.k..η.k..k.k.k.k -..η.k -.K.K ψ(η²-²) T VII- : sus DIRA qu ψ ψ vsus s ψ ψ. 47
49 T s s w w: ψ ψ s s u s ( ss u w ), ψ ψ us s us. T wv us ss s sus sss. F u vw, s wv us v uv s, w ws ss us. W w us s. Es s svs w (VII-). W u, = w ws w s u =. E : s( ) s( ) s( ) s( ) s( )s( )s( )s( ) E : s( )s( )s( )s( ) (VII-) s( )s( )s( )s( ) s( )s( )s( )s( ) s( )s( )s( )s( ) s( )s( )s( )s( ) E : s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( )s( )s( )s( ) E 4: s( )s( )s( )s( ) s( )s( )s( )s( ) s( )s( )s( )s( ) (VII-4) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) (VII-5) s( )s( )s( )s( ) s( )s( )s( )s( ) s( )s( )s( )s( ) s( )s( )s( )s( ) 48
50 s( ) s( ) s( ) s( ) (VII-6) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) T s ( VII-) s v s s.χ u s φ s su DIRA ss. As vus, s χ ws s ψ sussv w ss s w ψ=, s ψ sussv ss s w w ψ=. 49
51 .K.K.L.η.K.K.K -..K.K..η.K.η.K.K.K..η.K.K.K..K.K..η.K -.η.k.k.k..η.k -..K.K -.K.K.η.K -..η.k.k.k..η.k..k.k -.K.K -.η.k -..η.k -.K.K -..η.k.k.k -..K.K..η.K.η.K -.K.K -..η.k.k.k..k.k..η.k -L.η.K -.K.K -..η.k -..K.K -.K.K.η.K -.L.η.K -.K.K -..η.k..k.k -.K.K -.η.k -..η.k..η.k -L.K.K..η.K.η.K -.K.K..K.K..η.K -.K.K..η.K -.η.k -.K.K -..K.K..η.K -.K.K.η.K -..η.k..k.k.k.k..η.k -.K.K -.η.k -..η.k -..K.K.K.K -..η.k.k.k..η.k.η.k -.K.K..K.K -..η.k.k.k..η.k -.η.k -.K.K -.L.K.K -..η.k.k.k.η.k -..η.k..k.k L.K.K -..η.k.k.k -.η.k -..η.k -..K.K.K.K ψ.k.k..k.k..η.k -.η.k -.K.K -.L.η.K.K.K -..K.K..η.K.η.K -.K.K -..η.k..k.k -.K.K -.η.k -..η.k -.K.K -..η.k -..K.K -.K.K.η.K -..η.k -.K.K -..η.k.k.k..k.k..η.k -.η.k.k.k..η.k.k.k -..K.K..η.K L.η.K.K.K..η.K..K.K -.K.K -.η.k -.L.η.K.K.K..η.K -..K.K -.K.K.η.K -..η.k.k.k..η.k..η.k -.η.k -.K.K -..K.K -..η.k L.K.K..η.K.η.K -.K.K..K.K -..η.k.k.k -.η.k -..η.k -..K.K.K.K -..η.k.k.k.η.k -..η.k..k.k.k.k -..η.k.k.k..η.k -.η.k -.K.K -..K.K..η.K -.K.K..η.K.η.K -.K.K.L.K.K..η.K -.K.K -.η.k -..η.k -..K.K L.K.K..η.K -.K.K.η.K -..η.k..k.k.k.k..η.k -.K.K ψ ψ(η²-²) L ψ(η²-²) L T VII- : sus DIRA qu ψ ψ vsus s ψ ψ. 5
52 As vus, s s s svs w (VII-). I s w = w ws w s =. E 5: s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) (VII-7) E 6: s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) (VII-8) E 7: s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) E 8: s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) (VII-9) 5
53 s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) (VII-) A sus ss DIRA s s su ss. O us su v sus, w s s v w. II - Tv us A wv ss s s su w s wvs, w v sus vus s ( VI- ). O s w s, w w s ω = : s ( ) s ( ) s ( ) s ( ) + s ( ) s ( ) s ( ) s ( ) (VII-) w vs s: s ( ) s ( ) {s ( ) s ( ) + s ( ) s ( )} (VII-) s wv,, v wv s: s ( ) s ( ) s ( - ) (VII-) T s s ws: w w su s s w w (VII-), w vs s : s( ) s( ) s( ) s( ) s: s( ) s( )s( ) s( ) s( )s( ) s( ) s( ) s( ) s( ) s( )s( ) (VII-4) s( ) s( )s( )s( ) s( )s( ) s( )s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) (VII-5) 5
54 s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( )s( ) s( ) s( ) s( ) s( ) s( ) s( ) W u : = = A, w su -- su sus (VII-4) (VII-5), v su u: A s( ) s( ) s( A A A ) s( ) s( ) s( ) A s( ) s( ) s( ) s( ) s( ) s( ) A s( )s( ) s( ) s( ) s( ) s( ) A s( ) s( ) s( ) (VII-6) I s ss w w s, w v v sus,, ws s v w: s( s( s( ) s( ) ) ) s( ) (VII-7) III - O sus Bs sus ss s v s sus ws s s. Tw s s. I s, w s wv u ψ, w (- ), w (η/): s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) (VII-8) 5
55 I s, s w s wv u ψ w, w (-), -w (η/): s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) (VII-9) 54
56 VIII T wv- u W s, s sv qu s v: E 4 (VIII-) W s wv, s s wv v su s: E (VIII-) B u s s (VIII-), w u wv qus us s w s w sv s v: 4 (VIII-) : (VIII-4) O u s qu sus ss DIRA. W u s s, ss w ss (VIII-) sss sv, ss s wv. T quu s sv : (VIII-5) w u ss s sus w w s. As s (VIII-) ssu v, w sus s : : Wv us s s ss.,, : Ius w s,,. 55
57 : Mss A s su, w s ws s s DIRA s wv us. W s s su ss vus : s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) (VIII-6) I s su, wv us uss. Bu w v, sv, u s wv us s, ss s s s qu : s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) usu ss s qu,w : (VIII-7), u wv us s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) (VIII-8) E wv u w s s, sv s su, s u, s w us s s ss. I w w ss s u, w us v s s(.) = s(.) = s(.) = w us u s(.) = s(.) = s(.) =. T su s : 56
58 s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) (VIII-9) T wv u ψ us s : w ss s u, s : s( ) s( ) (VIII-) w s wv ss ². Bu su s us s (VIII-9) s s s vv quu, w s u, s u. I ws, w s s ss, s wv, w us s wv, ss ss. E s s s w ss wv s us qu sv quu, us qu s s w: (VIII-) I ssu s s s s wv- u w s, s (VIII-), ss ss, ss wv. I s, s s wv u ψ w s s s. T s us s s s: s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) (VIII-) I s s s us w w sv: (VIII-) T us s s s s us ss su w s s s w s w ss wv. O ss s ss, w s s ws s s ss su DIRA. T u us w s s, s v s: 57
59 (VIII-4) T u vs: 8 9,.. 7,8. / s 4,5. (VIII-5) T vu s us u u s s s vw. 58
60 IX T us DIRA () T ss s us s v vus s. I s : J J J J (IX-) Ts us sv qu: J J J () J (IX-) I - DIRA us s su A u s us w s su. W s s su suss vus : s( )s( )s( )s( ) s( )s( )s( )s( ) s( )s( )s( )s( ) s( )s( )s( )s( ) s( )s( )s( )s( ) (IX-) us, u wu us. F, w w sss: J s ( )s ( )s ( )s ( ) s ( )s ( )s ( )s ( ) s ( )s ( )s ( )s ( ) s ( )s ( )s ( )s ( ) s ( )s ( )s ( )s ( ) (IX-4) 59
61 J s ( )s( )s ()s ( ) s( )s ( )s ( )s( )s( ) (IX-5) J s ( )s( )s ()s( )s( s( )s ( )s ()s ( ) ) (IX-6) J s ( )s ( )s( )s( )s( ) (IX-7) W v sv qu (IX-). T s us s v s s. Ys: J J J J s( )s ( )s ( )s ( ) (IX-8) w, u s sv : (IX-9) s su: J J J J (IX-) W s s v sus s. Ts s u wv us u DIRA u u. I s s, wv u s : s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) s( ) (IX-) F vw, w w s wv u s uv s s, w w w, s u : s( ) s( ) s( ) s( ) s( ) s( ) s( )s( s( )s( )s( )s( ) s( )s( )s( )s( ) s( )s( )s( )s( ) (IX-) ) 6
62 T s us w: v qu ψψ s vu s. su s w s s w X X, w Y Y, w Z, Z, s s vu V s qu : V = (X - X) (Y - Y) (Z - Z) (IX-) T J us DIRA ss vu s u. I s ss: J s ( )s ( )s ( )s ( ) s ( )s ( )s ( )s ( ) s ( )s ( )s ( )s ( ) s ( )s ( )s ( )s ( s ( )s ( )s ( )s ( ) ) (IX-4) T E, w vu s, : E V s ( )s ( )s ( )s ( ) s ( )s ( )s ( )s ( ) s ( )s ( )s ( )s ( ) s ( )s ( )s ( )s ( ) s ( )s ( )s ( )s ( ) (IX-5) W w ss ss s s s s su s ss us -wv,,. X Z X Z Y Y (IX-6) w,, sv v s. U s s, s w : 6
63 X X Y Y Z Z s s s s s Z s X X Y Y Z X Y Y Z X Z (IX-7) u s (IX-5) s : E X X Y Y Z Z 8 s ( ) s ( ) s ( ) s ( ) s ( ) (IX-8) : V E s ( ) s ( ) (IX-9) 8 F s: (IX-) I s u v s u wv, ss us. Ts s quu, s sw (IX-9) s: w s u, s u v vs. F s (IX-9) (IX-) u: V E (IX-) 8 s E s qu, s ss s w vu: 8 V (IX-) A u s uv s, DIRA us us vu s, s. T u-v: 6
64 6 J J J J (IX-) s s s s (POYNTING ) v. I sss s vu V = u, 's us s v s ss s su u vu. II - DIRA us v su As, w s v su,, : ) s( ) s( (IX-4) ) s( ) s( ) s( us v w DIRA us: ) ( s ) ( s ) ( s ) ( s ) ( s J (IX-5) ) ( s ) ) s( s( J (IX-6) ) ( s ) ) s( s( J (IX-7) ) ( s J (IX-8) T u J s u s us s, uv s s,. I : ) ( s ) ( s J (IX-9) A u s s ² s vus, ss vu s. Us sv:
65 64 (IX-) s: ) ( s ) ( s J (IX-) : ) ( s J (IX-) T vu s s v ². I uus u s vu w s v v w s. T sv qu: J J J J (IX-) vs w su: ) ( s J J J J (IX-4) III - U DIRA us W w u us, us s. T sus DIRA qu w v s, w s v w: (IX-5) Bus us wv us u wv us, w : J J J J (IX-6)
66 O sv vu s ² ss s s w v, s u, s s s. Ts s s u w s u u s s. I, w w w s s qu ², s: J (IX-7) B u s sv, w u: J (IX-8) s, susu sss η: (IX-9 T u s s v s: (IX-4) Ts s sss s qu w ss w s su s. W s sv s ss su (IX- 5) s s quu w sv v s = squ (-). T s s w ss. 65
67 X P Ts, u HEIENBERG, u s quu s, ws u ss: " s ss w s u. F s vw, s w s s u Δ s u u Δ quu w:. (X-) W u v u u ws w v u v Δ s u u F, w u Δ: F. (X-) Ys, s s u s:..f. E. (X-) Ts s s us, s s u quu s u. su su s us, s s, s w s s su, s s s ss u su s sus. I w w s s su DIRA qu su s w s s s vus s: s( )s( )s( )s( ) s( )s( )s( )s( ) s( )s( )s( )s( ) s( )s( )s( )s( ) s( )s( )s( )s( ) (X-4) s qus u s. T su (X-4) v s s: s w,, w s s (, 66
68 , ) s () v. Ts s ss w HEIENBERG u. T v s, w us s su w us: sv s ss s w s ss. A s ssu s w sss : w suus s s. O ss s ssu, w, v su (X-4), vu s s w s u vus : J s ( )s ( )s ( )s ( ) s ( )s ( )s ( )s ( ) s ( )s ( )s ( )s ( ) s ( )s ( )s ( )s ( s ( )s ( )s ( )s ( ) ) (X-5) T s u vus s: - wv : - ss: - us :,, L us s (,, ) w vu s ss s u. L us ssu s w s ss s u w s s. T su s s v, s,, us : s ( ) s ( ) s ( ) (X-6) W qus: s ( ) s ( ) s ( ) (X-7) I s w su: us ss s s. I ws, w v w w, u w ss, w w s s, w s u s us s us s s. T s ss w w: vs w us w s u, ss us. A s s u vs,,. 67
69 Ts svs w us w s u s sus DIRA qu s w HEIENBERG u. Ts s s ss sus s s ws s, w sws s s s w qus s s. I s vs, u s ss w s v w s, v u w s ss s T s (X-) w s w : E. (X-8) vs s sw. I s wv, ws vu s s v (X-5): s ( )s ( )s ( )s ( ) (X-9) T s (,, ) s w s s u s s s w ss s u, s (X-6), vu s wv s w s s: s ( ) (X-) I s su s s w s u, s w s vus us ss w w su, w v s u s. 68
70 XI DE BROGLIE wv Ts s sw s sus DIRA qu u w uss Lus DE BROGLIE wv ss w. I ws w wv s quu s Rvs s. T s ssu v s O s w s v v. Hwv, s v s s O O s. W s su w w s, w s wv u u wvu. T s s s v s vv u. T s sv qus, uv s s: (XI-) Assu vs O, s u s s us u (XI-): (XI-) W u us, us su s: (XI-) W ws ss s us : (XI-4) T uv sv = () s w : 69
71 / ω Fu (XI-): s s us vsus us F wv w s wv, w s w s: ω φ = ω - (XI-5) w s v s v s s wv: v (XI-6) W ss s s v u us ω v, us s (XI-4): v (XI-7) ω > ω, s s s s. I s s s ss s s v, u s s w us w. W s, u v v vv us v s us: v (XI-8) W u (XI-) s s ω = ω, s ω > > ω. E s ω < ω. Gu v ss us u us, s s s v. As s s, s s sv (XI-) :.. (XI-9) 7
72 F w s s w s v u V: ² : v v ² (XI-) W u: v v (XI-) T w vs s, w Lus DE BROGLIE, w ss s s wv us ω s s s : (XI-) W s s v s v, ss s s v v, w wv s s u qu ω: (XI-) v O ss ssus (XI-) (XI-), w u ω ω us su w s: v F u v (XI-), w v: (XI-4) v (XI-5) I ws (XI-4) (XI-5) s ss v u v v wv's s v ss. Ts sus s vs ss quu wv s u. T s s s ss wv λ ss s wv qu ν us ω vs s vφ. F vus, w u s ss, u s u v, ss v s v. B us s v v ² sss s w s v u v s, s: 7
73 v v v v v (XI-6) 7
74 XII G DIRA qu Ts s w DIRA qu s v (A, A, A). Ts s s s u,..,,. W, s vus, su s s s w wu s u v. Fw s II, s DIRA s sus w qu w u-v s u: q T wv u ψ s -s w u s: (XII-) (XII-) T s γ, γ, γ, γ, v II, s sss, w u: (XII-) I s γ v qu (XII-), w ss qus: 7
75 74 q q q q (XII-4), s ss : q q q q (XII-5) A, w u: q (XII-6) w s ss s DIRA qu: (XII-7) I s s v ss. O wv us ( =,,, ) sus s ss s ws VI, :
76 75 (XII-8) w usu : = s ( ) = s ( ) = s ( ) = s ( ) (XII-9) = s ( ) = s ( ) = s ( ) = s ( ) (XII-) Us s u VI, w u us ss 64 qus w 64 uws w s s w: (XII-)
77 76 (XII-) (XII-)
78 77 (XII-4) T s s u sus VI, s ss ψ, s s sus ss wv us ψ, ψ, ψ. A us w s w ss su ψ, ψ, ψ. Ts w s sw su su s s, s s. s w v XXII. Pss ws ss su w s ss s ss. I s, s ss su u. W s u s v qu sv. W us ss s w qu sv ss v s. Ts s w s: - v s ϕ ws s. Rv suss s s s s ss. - v v (A, A, A) ws, wu su: s s u us. Ous s, qu sv s w: (XII-5)
79 Ius s s u ws wu v ss us. R u s s ws: (XII-6) I su u η v s ϕ s ss w ss η s u uv. T us us s su wv u-v u-v vs u-v : (XII-7) A s su- u-v su s s, s s qu sv (XII-6). T, w s v ss 64 qus w 64 uws s w qu sv (XII-6) s. Bu, s v v ws su DIRA qu ss. A ss ss DIRA ws wv s wv u w quu s s quu v, s s sus v s s (XII-,,,4). Quu s us s ss s w sv v w u s qu = sq(-) w sss s s. I su, s wv us s s, u s s s quu, s w sv v. Ts s w s svs s us,,, w u A, w v w ss: A( ) ( ) ( ) ( ) A (XII-8) T ss + - s s ss w s sv w su u : 78
80 (XII-9) Ts ss us s u, w ss su DIRA qu. Ts su s ss w sv qu: (XII-) (XII-) I s su v, s s s. W s us w w s. Fs DIRA qu: (XII-) DIRA qu: (XII-) (XII-4) T DIRA qu: (XII-5) (XII-6) T s vs, s: (XII-7) 79
81 (XII-8) s qu sv. Fu DIRA qu: (XII-9) (XII-) V (XII-) su s su DIRA ss s. W wu ss su (XII-), s ss su u s sus su w sus (ω) (- ), w wu w vus s ss su sus DIRA ss. I, s ss su s sus, us v sv qu, us u ss. O wv s s s s, s sw su w, w s s u s : s( )s( )s( )( ) s( ) s( ) s( )( s( ) s( ) s( )( ) s( ) s( ) s( )( I s ss w sv qu: ) (XII-) (XII-) ) 8
82 XIII T us DIRA () DIRA us sus qu s v w w us su s : (XIII-) T ss s us s w. Mu s qu, us vu s, J ss vu s. J J J J (XIII-) I, s us us sv qu: J J J J (XIII-) O s, sw w, wv us (XIII-) us (XIII- ), w sss: J J J J (XIII-4) 8
83 T sus su s ss s us s s. I ws, vu s s J s u s s. Ts su ss w s w s ss w s s VI, w wv su ssus sus s. I w s u sus wv us s, s u s u w s s s s, w qus. T s s w J ss vu s, vu V s : V E (XIII-5) I qu s s w (XIII-4) u s, s: V E (XIII-6) s, u qu sv : (XIII-7) V (XIII-8) 8
84 XIV us s W w sus DIRA qu w s svs sus v us s s s, w w s s w sus s s. I s s sus qu, us vu u v w s su. O ss qu sv w s u s s ssu vu s s w s s, sus DIRA qu v w s s ss s. T s ssu s s sus s v, u s s s s s v ss ss u w. Ts ws s u Lus DE BROGLIE u s ss: D w ssu s? Ts s ss w su (III) s s s. I s s, s sus s s, u s s s vs quu s. I uss wv u w s ss wv. I sws w HEIENBERG u s w ss us suus s s. F, s u w wv ss w w DE BROGLIE wv. 8
85 T E D qu s sus s s 84
86 XV DIRA qu s s T ss s sus DIRA qu s s w s w, w s, w sus ss s. I s s s w s, s s. Ev s, u sus HRÖDINGER qu, ss s su, vs sus w svs, s ss s s (Fu XV-) Fu (XV-): s s ss I s sus DIRA qu s s, s w us w s s. 85
87 Ev suss s sus, w us s DIRA qu s s. T s s v s w s s s: s s s s s (XV-) W u s: s s s s s s s s s s s s s s (XV-) O us w: s s s s s s s s s s s s s s (XV-) A, vs: s s s s s s s s s s s s s s (XV-4) T DIRA qu s s s w: (XV-5) w s γ : (XV-6) 86
88 T v s s s qu w w vvs w s s vs, θ, φ: (XV-7) s T ssu s w s γ, γθ, γφ. Ts qus, s s s, ss vvs w s,, vvs w s, θ, φ. T ss s ss, w us, w s s s: (XV-8) B u s s, θ, φ v (XV-4), w : s s s s s s s s s s s s s (XV-9) W s w s s,, : s s s s s s s s s s s s s s (XV-) W s ss w s s, w s s s: (XV-) Ts vs s s w vvs s s vvs s s: 87
89 s s s s s s s s s s s s s s (XV-) I s ss ss s qus DIRA qu s s: (XV-) T u s u v w: 88
90 89 s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s (XV-4) W s u vv, θ, φ, : s (XV-5) Ts u s s γ, γθ, γφ:
91 9 s s s s s s s s s s s s s s s s (XV-6) I su u s s DIRA s:, (XV-7) Dv ss DIRA w s :
92 9 s s s s s s s s s s s s s s s s s (XV-8) W u 4 qus w vvs ss DIRA ss s s:
93 s s s s s s s s s s s s s s s s s s s s (XV-9) I s - ss, us w s s s. T s ss s su s u (ss?) s u w su. W w sw w s s s s w s s ws ss ws su sus. 9
94 XVI KLEIN-GORDON qu s s I ss sus DIRA qu s s, w s sv qu w ss, wv, us w v us KLEIN-GORDON qu s s: ( s ) s s (XVI-) T sus s qu s u s us (), (), (θ, φ). I - su (θ, φ) Ts su s s s s Y us w s: - s Y, s u u. - s w s s : s su <= : = -, - +,..,.!! Y, P s (XVI-) 4 P s LEGENDRE s w. s s sus vu qu: s Y, Y, (XVI-) s T s s s s w: 9
95 Y Y Y Y Y 4 s s 6 5 5s s Y 5s 5 s Y s 8 Y s Y 5 s s 8 5 s Y Y 8 64 s Y Y 5 s 64 5 s 5 s s 8 s (XVI-4) II T s su Ts su s v s BEEL us () () w s u u. Ts us BEEL us: () () J N () () (XVI-5) s, v us: () () s s (XVI-6) T s s BEEL us s ws: s () s s () s () s () s s 4 s () s s () s () s () s s 4 (XVI-7) 94
96 95 I w () u sv () (), () s su s BEEL qu: () () (XVI-8) O quv w: () () () (XVI-9) v s us s. T us s s us w w s us ss,, u vs. B u v R = s BEEL qu (XVI-9), w sussv: ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( (R) R R (R) R R (R) (XVI-) III T s su I w s su u, s su vu qu: u u (XVI-) I s us su us s() s( ). IV - T su s s s (, θ, φ ) T KLEIN-GORDON qu s s s : ) ( s s s (XVI-)
97 us s s u u us, (θ, φ), :,,, Y u, (XVI-) T u s su KLEIN-GORDON qu s s s w susus: s,,, s,,, Y, u s,,, Y, u Y, u (XVI-4) B susu s ss (XVI-), s s : (XVI-5) A u s, s s: : (XVI-6) (XVI-7) As s s, s s s s : wv, ss (²) us. I su s s sv s s θ φ. Ts s su w ss, wv, us s s w θ φ. As s s s, s s sv w u s sus DIRA qu s s. 96
98 XVII E sus DIRA qu s s I vus s, w v sw sus D qu s s us ss: s s s s s s s s s s s s s s s s s s s s (XVII-) W v s u ss sus s s s s w, s sus us w qu sv ss us KLEIN- GORDON qu: (XVII-) Hwv, s s su v s sus v ss (XVII-). W us w us, us, s ss sus. W s us w svs sus s s. s w su: 97
99 s( )s( )s( )s( ) s( )s( )s( )s( ) s( )s( )s( )s( s( )s( )s( )s( ) s( )s( )s( )s( (XVII-) ) ) T s sv s -s s s s sus w s ws: - s s sss s s w ss wv. - s s sss s w s us. T s sv s wv- u. I s sus s s, w -sv, w v (us s ), quu, w s w ss s u, wv s, v vs. Ms s s us su KLEIN-GORDON qu s ss ss DIRA qus. Bs s w svs, ss v sw s s sus DIRA ss (XVII-) s s, w s qu sv (XVII-) s s w sus DIRA qu. T s s s w s s s sus, s s- sus v s T s s Y(θ, φ) su KLEIN-GORDON qu s qu s, s s θ, φ. I s su D qu. W w v w s, sus s s s sus KLEIN-GORDON qu. 98
100 XVIII E sus DIRA qu s Y- Y W s s s sus KLEIN-GORDON qu w s qu, w s u = =. T u s s s s v w s s, w s, w s ss v sus s : Y s Y s (XVIII-) W w w Y-, v, s ss, ss Y sus. T s Y- s ss w u v w s BEEL us : (XVIII-) ( ) J ( ) ( ) N ( ) (XVIII-) M sus KLEIN-GORDON qu ss u :,,, Y u, (XVIII-4) w s v us: u() = s() u u() = s() T suss vus v s w su w w v su: 99
101 ( )s s s s s s ( )s s s s '( ) s '( ) ( ) ( ) (XVIII-5) w w v : () = ()/(). T s s ss u wv-us u wv u ψ. Mss s w wv s s Y-. I ss suss vus. T s s s us w w w u. I s s DIRA ss susu s s. T qu sv ss w s su s : (XVIII-6) Ts s s u s s. I vus s, w v sw sus DIRA qu s s us ss: s s s s s s s s s s s s s s s s s s s s (XVIII-7) Ts ss v qus s us, u s us. I s wv sv u v v s su, s s w v u s s qus. T s qu, us s KLEIN-GORDON qu, w s s, w s v s s qus,, 4. V sus s. V s qu s DIRA ss:
102 s s s s s (XVIII-8) ) ( ) '( s s s s ) ( s s s s ) '( s s s s s ) ( ) '( s s s s s s ) ( ) '( s ) ''( s s s s s ) ( ) '( ) ''( s s s s (XVIII-9) V s qu s DIRA ss: s s s s s (XVIII-) s s s s s ) ( s s s ) ( s s s s )s '( s s )s '( s ) ( ) '( s s s ) ( ) '( s s s
103 (XVIII-) V s qu 4 s DIRA ss: s s s s s (XVIII-) s s '( ) s s s s '( )s s ( ) s s s ( ) s s s ( ) s s s s '( ) s s '( )s s s s s s s ( ) V s qu s DIRA ss: ( ) ( ) (XVIII-) As s vus, s v uss s us s qu sv v KLEIN-GORDON qu. s s s s s (XVIII-4) T u s s v w:
104 s s s s s ( )s s s s ( )s s ( )s s ( )s s s ''( ) s s s s s s s s s s s s s ''( ) '( ) ( ) '( ) ( ) '( ) ( ) '( ) s s ( ) s s s s s s '( ) s ( ) (XVIII-5) A s s(). -φ, s qu DIRA ss s w: ( )s s s '( ) s ( ) s ( ) s s s s s s s s s ''( ) s s s s s s 4 s s s s s s s s (XVIII-6) Ts w s u : '( ) ( ) () () ''() (XVIII-7) W w s s s vvs w s : (XVIII-8) O : (XVIII-9) Us s BEEL u ss (XVI-) :
105 () () (XVIII-) w = : ( ) ( ) ( ) ( ) ( ) ( ) ( ) (XVIII-) B s s s su w (XVIII-9) s: ( ) (XVIII-) W s sv : (XVIII-) V su DIRA qu s s s. As s s, v, s su us ss w qu sv s s. A us s, w s Y: Y s (XVIII-4) I s s s vv us, s Y- s s φ. Ts us squ: w su s u wv-us wv u ψ. T su s DIRA ss su s u wv u ψ. W s su vus, w wv us s s us s : s ( )s s s ( )s s s s '( ) s s s '( ) ( ) ( ) (XVIII-5) 4
106 W w s s φ s. Us v us s (u sw ), w ss s s sus. T s: ( )s s ( )s s (XVIII-6) ss w sv - s s usu s "u". T s: ( )s s ( )s s (XVIII-7) ss w v - s s usu s "w". 5
107 XIX O sus I - T s Bs sus s vus w. I s v su u su s s, s ss sus ss s. DIRA ss s w s s s us, w u w sus su sus ws s vs v. W s w w s 'w' s w (su ) su (XVIII-5): s ( )s s s ( )s s s s '( ) s s s '( ) ( ) ( ) (XIX-) W (su ) su s s wv u ψ : s ( )s s s ( )s s s s '( ) s s s '( ) ( ) ( ) (XIX-) ): W u su : (su ) + (su 6
108 ( )s s s ( )s s s '( ) s '( ) ( ) ( ) (XIX-) Ts w ( + φ) ( + (-)φ) s φ s w sv v sw s. T vu s w ssv wv. A wv s (ω ) s v ws sv : wv s ( - φ) s v ws sv φ. A wv s (ω + ) s ss ws v : wv s ( + φ) vs ws v φ, w uss s 'w' su (XIX-). I s ss su sus s ( + θ) us s sus sθ sθ w ss w s () s () us θ. II O sus A sus KLEIN-GORDON qu, v, vus w. T vus s su sw s su s = = sus DIRA qu. I us u s su sus. A s s Y- Y s sws s s w sus w w. II- - Y- I s ss w s Y-: 5 Y s s (XIX-4) 8 u T u s v w s BEEL us : s s (XIX-5) 7
109 s s (XIX-6) M sus KLEIN-GORDON qu ss :,,, Y u, (XIX-7) w s v us: u() = s() u() = s() T w s vus s ws w su: s s s s s s s s s s ' s s s ' s (XIX-8) w w : () = ()/(). II- - Y I s ss w s Y w: 5 Y s s (XIX-9) 8 T s vv us, s Y- s s φ. Ts s s vs Y-. T w su s : s s s s s s s s s s ' s s s ' s (XIX-) II- O s I s sv s u s su w >, s s s w s u us w 8
110 s ss. I s : I s s sus DIRA qu, s ss s s vs s s s w su u. 9
111 XX ss sus s s T ss s s s s ws v s v ss sus s s, s. T v u sus DIRA qu s s s w' ss w. s s s w. Ts s s v sus w sv s. Hwv w w v v u s u v s sus. I P s L us s su Y-: s s s s s s s s ' s ' s (XX-) w s s BEEL u : s( ) ( ) ( ) s( ) ( ) s( ) s( ) ( ) (XX-) ( ) ( ) w w () = ()/(). A u s, wv us s s :
112 s s s s s s s ' s s ' s (XX-) T us v v vu v = w s s Bss u s J. W w s susqu suss sus. W suss ws uv s s. I s s s s u : s wv u s s squ vu s, s vu vs. T s s ψ ψ s w ss wv. T s s ψ ψ s s us s, w s s ss. Ts us s ss vs s, θ, φ. T v w s sus s u O s: us us φ. T v s s us vs s, s s: us us w. T θ v s us s, w w ssu us ss w s v s. T wv u ψ ss w φ: us ssu s v us. W w ss ψ wv u us. Ts ss s su ψ wv u s s w ss s "u" s "w". I s s s su θ, s w s s. W φ = π, s (XX-) u s s, w suss w ss s w s. W w s s u u s u θ = 45 θ = 5 w O s. W s us ψ wv u: s s s ' (XX-4)
113 F vw vu s, θ s v u: s s A( ) (XX-5) Ts u s sw u (XX-) w:, A(θ),5,,5,, θ Fu (XX-): Rs su vu s us vsus θ Y Y- s s T us s sws u θ = 45 θ = 5 s. I s s, su u s vus ss s, u vu s. Ius s wv ψ u: s s ' s (XX-6) N s s ss su s s. T s s s s. I's ws s ss s u s, wv us w s s w ss uv s s: s s s s s ' s s ' s (XX-7)
114 T s u w wv u s s, us s s: w s s u ( s () = ), s s u (s () = ) v vs. I, ss, s ss w s s. Du s w s, s us. II P s / W w DIRA qu s qu ws sus ss s v. W us sus s qu s s, s s v s. Y- : T su w s v s s s Y s s s s s s s s ' s s ' s (XX-8) w s s BEEL u : s s (XX-9) s s (XX-) w w () = ()/(). A u s, wv us s s, w w s vus, s s s ss s su:
115 s s s s s s s ' s s s ' s (XX-) T s s φ: wv u ψ s π, ψ ψ wv us 4π. T s ½ s s -s us 4π u s s. I s su (XX-8) w s w s s ss v w s u. u s s, s ss ψ ψ s u 4π s ψ u s s. T s w suss (XX-8) su ws s w ψ wv u: s s s ' (XX-) Ts wv u s us φ. θ s s, w u w s s u φ, w v sv: s s s s s (XX-) w vs θ su s: (XX-4) A : θ = 54,7 (XX-5) F vw vu s, θ s v u: s s A( ) (XX-6) Ts u s sw u (XX-) w: 4
116 ,6,4 A(θ),,,8,6,4, 54,7 5,7 θ Fu (XX-): Rs su vu s us vsus θ Y Y- s s s ½ I s s s s s u u. III «/» O s sus DIRA qu s Y Y-, ss w u u s s u. Ius s s wv u ψ w s : () s s s '() (XX-7) s ss s s θ, θ vu w s us s u. Ts s quv sv qu: s s s s s (XX-8) W vs θ su: (XX-9) I us u s s v qu u u s ss s s /. T qu s w w s, w u, w w s. T sw, w qu u u s O s : 5
117 (XX-) u u quu s s w: (XX-) A θ s v s: s (XX-) Equ w (XX-9) v (XX- ) v ss qu s u u s v s: s (XX-) 6
118 XXI DIRA us E sus DIRA qu s s sus w sv, w s s u ss u-v vu s us u. J J (XXI-) W v s s s u DIRA qus w s: (XXI-)) I w: T,,,,,, (XXI-) B (XXI-) w (XXI-), w u-v u DIRA: J (XXI-4) w γ μ DIRA s. T ss sss s us s s, w us us DIRA s s ss. Ts s s,, θ, φ w s w. 7
119 8 (XXI-5) s s s s s s s s (XXI-6) s s s s s s s s (XXI-7) (XXI-8) Ds sss s us sw w: :,,,,,, J J (XXI-9) :
120 9 s s s s s s s s J s s, s s, s s, s s s s s s s s s s,,, J (XXI-) θ: s s s s s s s s J s s, s s, s s, s s s s s s s s s s,,, J (XXI-) φ: J s,,, s J s,,, s J (XXI-)
121 Ts sss w w sus w sv. T us u us. s us s w, su vus : ( )s s s s s '( ) s '( ) ( ) ( ) (XXI-) u J : J J ( )s s '( ) s s s s ( ) '( ) ( ) (XXI-4) O s u, vu s s s v φ u J : J s s s s s s s s (XXI-5) J F su, w v ψ = : s s s s (XXI-6) T s vs u us wv us. A s, s ψ ψ u s. W u: J (XXI-7) u J θ : J s s s s s s s s (XXI-8) F su, w v ψ = :
122 J s s s s (XXI-9) T s vs u us wv us. A s, s ψ ψ u s. W u: J (XXI-) u J φ : s J (XXI-) F su, w v ψ = : s J (XXI-) W : J ( ) s s '( ) s ( ) (XXI-) w ssss us DIRA, w w s us ss vu s s, w s sv. Ts s s w s s: J J s J J s s (XXI-4) I s v, us s s v, s, s. A sw ss sws u s s : - T vu s J s, v s φ. O, vs w θ, s s. - us DIRA w θ, s w w s s. - T D u φ s -, s w w u u. Ts w s u us s φ. I, w s s, w s.
123 XXII G DIRA qu s s O sus D qu s s s u w u s su sus w s s s u u-. Ts s ss s s XII. W s su s s sw. W us s qu sv w w s v. W s s s ss KLEIN- GORDON qu v u LORENTZ s: A q A q (XXII-) I s s, Aµ s s u- (ϕ/ A, A, A). I w, w u, s XII: q (XXII-) T v qu (XXII-) (+,-,-, -) vs us: (XXII-) O s :
124 (XXII-4) T s s qu s, ws v s. W w s s w ss s. I T s W s s s, w w w u v, w s u η = η = η = qu (XXII-4): (XXII-5) T u s s vs L : s s s (XXII-6) I s ss s s XVI s s su s: (XXII-7) I s u w XII ss svs ss XII-,,, 4: s ss s su s () s() ws qu sv v (XXII-7). Pss sus : s s (XXII-8) T s quu w sv v.
125 B s s s (XXII-8) (XXII-7), s sv w us v ss D s s s s : O s: (XXII-9) (XXII-) I's XII, ss s s. T ss D s s s s w: s s s s s s s s s s s s s s s s s s s s (XXII-) Us su (XXI-), su s s ( )s s s s s '( ) s '( ) ( ) ( ) (XXII-) I s ss w sv: (XXII-) II T v F (XXII-4), w u KLEIN-GORDON qu w s s s qu s v : 4
126 (XXII-4) O s, s: (XXII-5) T ss s s s susu L vvs u XV s s s s s s s s s s s s s s (XXII-6) T v s s w s: s s s s s s s s s s (XXII-7) W u KLEIN-GORDON qu s s v s s _ s s s s s s s s s s s s s s s s s s s s s s s s s (XXII-8) 5
127 A u s w vs, w : s s s (XXII-9) I w qu wv u ψ s s s s, s s w ss sv : (XXII-) Ts s s us s (XXII-7) s. I s u v u: s BEEL us s su s s sv (XXII-). I ws u su DIRA qu s s u s v u u. 6
128 XXIII us I O sv T s sv ws s us. I s w s: s sv u, sv. B u s sus. I- sv I s su- us u v: v v ~ P v E E E (XXIII-) ss u : E² - ²² = (XXIII-) s s s w s ssss. Ts s s qu s ss squ, s w s vv, w s s: E (XXIII-) I w s s, s us s, s s qu s ss. I w s s, s us s vu ss s v s s (XXIII-) (XXIII-) v. W w ss s s quu s, s s ss s sv : 7
129 ² ² (XXIII-4) s vs w s qu ² ; (XXIII-5) W sw G, s s sss u s s s, ss s s, w us wv v s v s (XXIII-4) Bus vs DIRA qu: μ =,,, (XXIII-6) s v u, s ss sus ss ss,,,,, qu sv (XXIII-4). II O DIRA qu sus T sus DIRA qu s s. I s s ss ss,,, s. O s v, s w ss, u s s ws s ss ss quu s. I u, s s u ss, s squ wv us s ss. I, squ wv us us vu s. A ss s u u s s, w sv v. F, s u E s v, v s s us us s v. T ss s s s sws w ss w sus DIRA qu v ss s w s s. T, w s qu ss squ s, squ vu s, s s u = sq(-), w s s s qu w v. Tus, s sus s s, s u = sq(-) s s us u v. I, DIRA us s : us vu s, us u sv qu. III O v 8
130 I w ss vus s ss us s s, s v s us s us us s s s. I s u, w u s ss s w s (III-) (III-) w ss w s s. Ts w ss s w ss s (-ω). T w: E (XXIII-7) s : E E (XXIII-8) T us s w s w ss w s s s s s ss v. Hwv, v sws s ss s : s s s. T, s - w s s ss ss ss w s ss. squ, ss, s v v s. W s v s s, ss ss. Ts su s w u s s s v v s vu s u. T w v s. L us s ss RL u. I w su s u, s s u-s w s. A u, s ss ss R u s us ss. O ws u ss s u s u v ss (-R). Ts ss su us vs v s (-R): s v v. T w PR ss ss R s s w: PR() = R I²() (XXIII-9) s s w s u sv. 9
131 Pw P(-R) v v ss s w us: P(-R)() = -R I²() (XXIII-) s s w s u v. u v sus s ws: Nv su v ss u L : E s ss w s Psv E ss sv ss T s s s ws: sv w sss w ss ss s, w v w s w s s ss. I s s s, sv u ss s: PR() + P(-R)() = R I²() - R I²() = (XXIII-) I w, w wv us, w s qus ψ+ ψ- s squ w, s qus s: P () P R ( R) () RI () RI () RI () (XXIII-) O s ss s sv v us ψ+ ψ- qus. I ws vss ss su w s qus ss, s s sss : P () R P () R P ( R) P ( R) () () RI () RI () RI RI () () (XXIII-) T w P() ss u vus qu s u: P() RI () (XXIII-4)
132 B s ss, w sv u s w s ws sv: w qu ws v s us D us. W ss v ws quu s, s v qus: w s u (v ), w s ss (sv )? I ss ss ss s w vuu, ws s ss. U s ss, u s s s ws: Nv v vuu E s w Psv s vuu....vuu..... A s s u ss ss w u w quu uus vuu, vs s uuus sv v. I sss quu w, s s s w vuu. W u s s s su s w s vuu v ss sv -s. IV us Quu s ss v ss w s u s wv- u. Bus DIRA qu s qu ss s, v s w s s w, w s s, s sus. T s qu s s, s s v s, s v us s s qu. sus v s s sv. s s ss sus s s, s ss sw su s ss vs s ss. T ss sus s s s w ss s sus w vs s.
133 us s s s s ss w vus s. T wv- u s s w ss wv. T s s s s sws s uus s w sv v. I s s, s us ss, w w ss us s sus s s. T s ½, s s 4π v s s s s sus: w s us w s π u s s, s us φ wv- u u 4π. T u s s usv s s s, u v, ss us v u s, w s su sw s w v s w s. w v su u s w s w qus, s sus ss u w u s s.
134 Fu s
135 4 XXIV T DIRA qu v : ss M sus DIRA qu s vus s v v v ss w s u s,.. s. W w s uss ss s u., s uss s sus v v. Nw, w w v ws sus w s s v s. u sus su us s u s, u v s. T v ws su sus, s ss s ss s, w ss s sus w u. Ts s s s s v s w s v vs, u s s. Ts s s w, u s u s sus w s. W s s ss DIRA v, w s vs s : q q q q
136 5 (XXIV-) As s u, s : q (XXIV-) I s, s w ss: - F : A A A A A A A R B B B B (XXIV-) F : A A A A G E E E E (XXIV-4) I vu -s, w ss (XXIV-) v : (XXIV-5) T, w u:
137 6 w (XXIV-6) D ss s w w u sss: (XXIV-7) W u s w: M (XXIV-8) T u ss s s : M M (XXIV-9) O s: M M (XXIV-) F w w u :
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