Lu at. a l. iz io. e a. L n. e g s. t p e. e c c. t g. u n. t o. s o

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1 OkRdgN Lu z L l l L by L E g u P g D p d hnul M T h h u l g y I m u f f h (MIT) Cuy f Luz Ll, Ok Rdg Nl Lby. Ud wh pm.

2 S g:chdih (Ifff) (. A O ) C u h u f w E l v h hvg d S b g m g g d h d 2. F kz mp h d u l u w u v h hzd by dwv(,l w g gy m ) k ψ = ( R h l v h u l d u ) ymhd

3 3. F N ul h g, wh m gyd p h lby ym, h l wv ( dddhly) " = # N $ =!! k #R! R Lby p f h h ulu 4. Ch g ff ly h gul dbu f d u. I d ff h l g ( u vdh g)!! # R

4 SmplSym Th d wv vg h d mb f h wv dad Bdgvby ψ (,θ,ϕ) k k( +BC ) + BC Th g lgh h m f bh ul.

5 S >> BC, + BC h dm bpldby Thgm BCgv BC = dθ ϕ SuggdHmwk: Shwhbvxp H: Clul h gl bw w v phl d. Thl d wvfu k ψ (,θ,ϕ) = [ + kd θ ϕ ] Dfghg fu f [ ( θ, ϕ ) = + kd θ ϕ Thdfflg ]

6 σ (θ,ϕ) = f (θ,ϕ) 2 Th dffl g p ulu f u mplym bdby ughxpf f ( θ,ϕ) whf ½(wul) σ (θ,ϕ) = 2 [+ (kd θ ϕ)] 2 Suggdhmwk: Bhv f σ (θ,ϕ) f kd << (lw gy)dkd>>,(hghgy)

7 C ϕ = d σ (θ,0) = 2 S 2π k = λ σ (θ,0) = 2 h pl f 2 [+ (kd θ)] 2 ϕ = 0,. d + (2π θ) λ., Whhmxmumfσ (θ,ϕ) u wh λ = dθ =,2,3... Th hbgg lwfumplym.

8 Iglhu: Nuddbygl θ Bgg Lw λ = 2dθ =,2,3...

9 Nhf: () λ > 2d Bgggpbl (b) Mxmumuf λ = 2d mx ;h h Bgg uff Wkwh λ = (m) E(V ) Suggdhmwk: Shwh λ = f ( E) bv Th xpfh Bgguff d mx = Å=0 8 m 0.43 E(V ) (Å)

10 Clul d mx =?

11 (B) IhElSg:. Sg by dl ul 2. Nulp ( h I h f 3. N ulpg ( Cyl) ) N dl ul (ug wh mplym) mpl ym w hv b udyg h g fw dlul h wll w d g lgh d 2 Thdfflg σ (θ,ϕ) = + 2 kd θ ϕ 2 2

12 σ (θ,ϕ) = [ (kdθ 2 ϕ)] Mxmum: σ (θ,ϕ) = ( + 2 ) 2 2 mx Mmum: σ m (θ,ϕ) = ( 2 ) 2 2 = 2 Iflyhgp m d σ (θ, ϕ) = 0. m Th z σ ( θ, ϕ) = 0 d h pf h g.

13 I gl f umb N f ul wh g lgh ( =, 2, 3,...,N) h dfflg p ul : σ (θ,ϕ) = N N 2 G (k,r ) = R Pfh hulu * If G h mplx jug f * * G G = GG = Sm df: < >= N N = G h

14 Th xp f σ (θ,ϕ) N N σ (θ,ϕ) = m G G * m N = m= B yug = whv ( < >)+ < > b w N σ (θ,ϕ) =< 2 > < > 2 + < > 2 G N = Suggdhmwk: Shwhxpbv 2

15 Thg σ = Th 4π σ ( θ,ϕ) dω σ = 4π(< 2 > < > 2 ) + 4π < Th h d h :. Ch. σ h = Ih σ h 4π < > 2 = 4π(< 2 > < > 2 ) > 2

16 (b) Nulp Whyh uff?? Pl u ulu dpd h fhpv. V () I. I ul p u p ( /2) Chl p: J = I + Thf: J + = I + / 2 d J = I /2 J um f I d h

17 Thlpfgv 2J + g(j) = (2 +)(2I +) Fh g d g + = J + I 2I + I + = 2I + d J whv

18 Th p h d h. Sph σ h = 4π( g g 2 ). Sph h σ 4 g g + ( ) 2 = π + Exmplf H + = 5.3 wh fm Clul: h σ =? fm = fm =0 3 m d I =/2 h σ =? σ =?

19 I I h l C h E m ff l g l yg g y l v d l l f h ff h l d h f h g w y l v, l l d l g. N l h g h g, d L xm. p R m b l m l : u T l h ( E l g m y p, l V L b v l ). T f h d.

20 = 2 d = ' ' 2 Thdum: mm2 µ = m + m 2 () Vblmd: Aum h m m gh byl d m2 bud pguh F = k(x x 0 )

21 Cll d 2 x = k(x x d 2 0 ) x = x 0 (w + ϕ) k w = ; w = 2πν m Th gy lvlwllb E 0 = w 2 3 E = w 2 5 E 2 = w 2 Quum Mh d 2 ψ 2m + (E kx 2 )ψ = 0 dx E = w( + ); = 0,,2,... 2

22 (b) RlMd: () E f = mυ m 2 2υ 2 υ = w d υ 2 = w 2 h Cllgyfhym

23 E = 2 I w 2 wh I = m m 2 2 Ug = + 2 d m Th pblm dud bdy pblm + m 2 2 = 0

24 Thgulmmum L = mυ L = m 2 w L = Iw Th gy bm L 2 E = 2I () L 2 = 2 Quum mhvwp l( l + ) h gy wll b : E 2 = 2I l(l +) wh l = 0,, 2,...

25 Vbl RlEgyLvl

26 I h l g p h vb md f h ym ( yl f ) my hg du ll wh u.thvbl gy quzd lld ph. I m l ym wh vl ul p pbldfy dvdu lph. Ih u h p f ph pum (ph dbu) uu lly fufhfquy w ( 2πν). Th gy f phf fquy w w d hgypum f ( w)

27 MIT OpCuW hp://w.m.du Nu I d Appl Spg 200 F fm bu g h ml u Tm f U, v: hp://w.m.du/m.

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