Chapter 5: Quantization of Radiation in Cavities and Free Space

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1 Quu O f Ph Ol Fh R Cll vy Ch 5: Quz f R Cv F S 5 Cll ly 5 Cll Cvy ly Mxwll u f lg J 4 h lv l C fl vy W f h g f h vy Th vy u luly ll W l u h J Cvy F Mxwll u v h wv u Th v u lv h f h fu h vy I w wh h v l l f fl Th l u lw 5 Sl Pl W u v l l S f hg fl

2 Quu O f Ph Ol Fh R Cll vy 5 Gug Tf Gug Fxg Th fl hg f w h fllwg f F F wh F y l fu S h g f f h h f I h w h h f uu O l h l h uu I -lv ly h l Iu f l h ll gug fxg h ul h f gug ll h ul gug I h ul gug Th l fl v w T I h ul gug T I fllw h T ll h lgul l fl u h hg y whh T ll h v l fl u h - u y J Th v l l v w T I h ul gug h v l ly v I -lv uu ly T wh h I h Ch wll l lwy z wll l z hul u T I h ul gug wh J w hv Mxwll u gv N h fy h wv u

3 Quu O f Ph Ol Fh R Cll vy 54 Cvy g gvlu T fuh w f h g f h h h wv u h g l h g gvlu Thf Th gfu u l fy h u h whh fllw f h ul gug W wll u h h g h lly l fu Ohgly Rl f h g: C w ff g Th fy T h u f h f h f u wh g g h v y C C C gg v ll w g Ig y w h lf h Thf f h 5 Thf gv g ff gvlu hgl h f 5 v If lz uh h h

4 Quu O f Ph Ol Fh R Cll vy 4 wh h vg lv l y h 55 Fl x ug g S h g f l h f ll v v fl lwy x y v v fl ul f h g Suug h v x h wv u w g Mullyg h y g v ll w g Th v u h h lu O uvlly lx -h 56 Fl l Th ll x f h fl gy N h Thf

5 Quu O f Ph Ol Fh R Cll vy 5 If f h F Mxwll u w h fu S h vl fy h u Cg h v u wh h f l h ll w h hy l! 5 Cvy Quu ly 5 Quz f Cvy Fl F ll fl w v h fllwg x f h gy h y gv y W ful l vl f y h hy uz h fl N h h fl hv l l h ll SO N u h h x f l gy h h f SO u h y l l S w y uzg y h fllwg : h y vl h ul- u l w F ff l h u l Th l f h fl h f SO f u f h fl

6 Quu O f Ph Ol Fh R Cll vy I fllw h Th h v x hul h g S f xl h l h Shg u wul wh h u f h 5 gy g gg S ll g hv ly w ly Th l f gl h g f h l Fllwg h u Ch 4 w hv gy g wh gy Th g f ff g y ull f Th gu h gy Th gg 5 Th Ph O uzg h lg w h h gy f gl f h fl wh fuy ly vlu f h h y ull f h gy ly ull f Th wh ll ly wh y gy vlu y g g h fl lu uu fh Th u u f gy wh h h wh gl h h ll l x v h gu f fl wh gl h h gy 6

7 Quu O f Ph Ol Fh R Cll vy wh w h h gy wh h gu f fl h h u ll h gy ul Th Th ll h u f h u gv h u f h â â ll h u u hy h u f h Th w! Th ll h u hy g f h u h l h wv h u h ll l gy x f fl 54 Mul S ul uu wh h 4 h 5 h w 4 5 S 4 5 O y w 4 5 Th vuu h gu f ll If w hv wh h h 4 Th v u I ylly w O ly w w h h hv -z h u f h wy Fw xl gv lw wh h 7

8 Quu O f Ph Ol Fh R Cll vy 8! wh h whh l u f h Cl Rl f h Ph Nu S: full lw l l f h l l Bu y l l uully lg wh h fw S f y h h l l Ohgly Rl f h Ph Nu S: W f h vlu f h u S h g l fu hgl h ly vu wh hul Bu g f Ĥ w hv 55 T Dvl f C Du O Th vl f h u fllw f h g u 56 Fl O Th fl hyl vl hf y W w g u ug

9 Quu O f Ph Ol Fh R Cll vy 9 N h ll fl Nw uu wh ll h 9 9 f h vg l fl f h Th lg u f h h 9 u h z vg vlu f h l fl Thf h h u lly wh g f y yu ll h 57 uu Fluu Th gu f h gy v hugh h h h Th gy u wh ll vuu fluu; h gu h l g fl hv z vg vlu u vg f h u f h fl z I f g ulv u u hw Th l vuu gy lug u f ll h whh f Th fy l x ly h ff g u lu g W w whh h u vl f vlu f ll h wy u Wh vy lg h vy vy f v lgh l l h h h Pl l f - Ny w f uu ly vl uh h l l

10 Quu O f Ph Ol Fh R Cll vy 5 ly F S 5 Cll ly F S Mxwll u f Th v u ul h wv u ug f ul gug ll fl v vg f l wh I fllw h S h wv u f 5 F-S g gvlu W f g f h h wh gvlu Th gv u l fy h ul gug Th gv w f l wv Th g lz vy lg x f vlu ll hyl ul wll u u f Th gh h v l wv gg h f h

11 Quu O f Ph Ol Fh R Cll vy v wh h v l h l fl lz h f h u v N h Thf h gvlu f h l wv lu S h f u ly gu w wll w Th l Th f fl lz ul h f g f h l wv gv y h v F h h w uully hgl ul h hv O h y w uh f h lz u v ll h F xl f x g h x- h h y z O y l h y z y z Th l wv g f l h f ll v v fl Thf h fl x h l S l * u hv I v h K h g y h u v hv l lh wh h C u v x ŷ ẑ 5 P Buy C F f F h u f lul uful u h f lg x f h vlu ul W l u h h f f h x

12 Quu O f Ph Ol Fh R Cll vy wh h f S h g u gl-vlu vywh h fllwg uy u hl x x x x x y y y y y z z z z z Thu h v ly hv vlu Th ly uh llw vlu u f vlu - Thf g h h ff llw vlu u vlu - h u v f h f l y h gl Th fl w w Ohgly Rl f h g: Th hgly l f h g δ δ S h C f z y x Th fu fllw x x x z y x z y x z y x Flly h l g fl 54 T Dvl W lug h x f h u

13 Quu O f Ph Ol Fh R Cll vy g Mullyg y h gg v ll ug h hgly l f h w g 55 Fl gy Th gy f h fl fu fllw F w y u h g v ll F h xl f f h u g f h g/u v l vywh y l h fllwg l Th fl ul Th x f gy h lx u S ll ff f wh yu hv h If f h h x f h gy

14 Quu O f Ph Ol Fh R Cll vy 4 56 Fl Mu I ll lg h u f h lg fl P g h l P 57 Fl gul Mu Cll lg fl hv wll-f gul u Rll h h gul u f l wh u v wh gv Th ll x f h u f h lg fl f vu S P Th ll x f h gul u f h fl J ully h f f h g gv h hgy f f h v x w J 54 Quu ly F S 54 Qulz f R F S Th f h uz f y y h f vl h f u l I uu ly h vl h fl h u hf I ll lg Th v w y f h fl l I uu ly h fl wll v T uz w h fllwg ul- u l

15 Quu O f Ph Ol Fh R Cll vy 5 I fllw h W f u f Th gv 54 Fl l Th fl gy w f h u 4 Th vuu gy Th vuu gy y hf 54 T Dvl f C Du O Th vl f h u fllw f h g u

16 Quu O f Ph Ol Fh R Cll vy Fl O Th fl f u h fl Th f h l g fl 545 gy g Ph Th gy g wh h h 546 Mu f Ph Th fl u P g h g x f h fl g P Th ly -z

17 Quu O f Ph Ol Fh R Cll vy 7 P I h Shg u P Nw w h f h gy g h h u l u g W vlu P Th ul P Thf h u wh gl h h wh wvv 547 gul Mu S f Ph Th ll x f h gul u f lg fl J Th v x f w u Th l gul u Th gul u h gul u Th w h ly l ly v Th h gul u f v l y l lly f y lg h gul u h f f h l Ml l l h hv f h u w Nvhl f l l l wv wh l f h f h ully gg hv y l h h gul u fu ug h x v ll u hg u h gul u f T h lly w fllw W u h h fl v vg f W f h ll x f h gul u v f fw ul J

18 Quu O f Ph Ol Fh R Cll vy 8 Th f uully f wh h h gul u h wh h l gul u I g w S J wv v h u l F l wv h hw z S f l wv w wll h x f h gul u S uz h fl gv y g h v x h Ŝ S g v v f h u lz v w S I h Shg u S Th Ŝ gl h wvv u gl h lz Rll h h gl h wh wvv wh l lz h f h u v Slly gl h wh wvv wh l lz h f h u v Th h h lly lz l wv g f Ŝ W f w w u g fllw R R N h fllwg u l

19 Quu O f Ph Ol Fh R Cll vy Th R R R R R R gl h h gh-h ully lz Slly h gl h wh wvv l u f lz v wh 9-g h ff w h w lz I f gl h h lf-h ully lz I f h w h x f Ŝ S R R I h Shg u S R R R Th Ŝ w gl ll C gl h I g f h Ŝ wh gvlu S W y h h gul u f gh-ully lz gl h l wv Slly h g f Ŝ wh gvlu hf h gul u f lf-ully lz gl h l wv Th f h gul u lwy lg h x f g Th f l l gul u u u f Thf h f h hv w vlu + - h h wh gh-ul lf-ul lz 548 P f Ph F h vl h f h h g y f g f h u vlg z v I f h ffuly h f h v l uh l u f v l lwy f f whh h l vg vy lwly h f lgh h f x g h -lv g Bu h g l lwy vllg h f lgh hf guly f wv y f h f h u h fllwg u If h h g f h wh h ly f g h h l vl wh h l W wll u h u l wh w u h l Ch w u f wh g wg wh yg llz h h C h gl h 9

20 Quu O f Ph Ol Fh R Cll vy Th h l wv hf u Wh f w h u f l wv llz? Wh h h v h fllwg Th gl h xl u f l wv wh lz h f h C u v ê Th u hw llz h h h l If lly llz h w ul h w g f h h O wy w h v u y yg h h ff l lz lg ê Phylly h g h l wh lz lg ê gv h S w vlu h fllwg x l If h h y llz g x f h h w hul x h w l l W vlu h x l lw Th w ll h v l fu I llz l l fu u u O w 4

21 Quu O f Ph Ol Fh R Cll vy Th w u g whh wul u x f g h h g l u v O u l wv u l fu u v l wv u u l fu Th gu hw h h llz 549 Fl Cu Rl Th ul- u l g h fl x h ly f ulu u C f h l g fl Th ul- u l w h w Ng h f y w v h -u w B B wh h v-cv yl wh h y h gv f y u f h g w Th ul vv f l fu Th yl f vv wh h C ul x y z Th ul hw h f h l g fl u ll u ff f h l g fl u Oh g u h fl u l ff l ff Suh u l hw whh u ulu u fl ff l l Of u wul x lgh f lvy h f fl u l f ugh uh h gl ul vl h vl w h u h uh u hul ff h h I h w ll fl

22 Quu O f Ph Ol Fh R Cll vy u u f -l vl wh g h x f h l fl w g T vlu h v x w vlu h gy f h fllwg x l 4 l Th gy f h v x 4 Flly h fl u 4 Th v x hw h h u -z ly h lgh wh hf h fl u f -l vl

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