EQUATION SHEETS FOR ELEC

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Lesley Shelton
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1 QUTON SHTS FO C 47 Fbuay 7 QUTON SHTS FO C 47 Fbuay 7 hs hυ h ω ( J ) h.4 ω υ ( µ ) ( ) h h k π υ ε ( / s ) G Os (Us > x < a ) Sll s aw s s s Shal z z Shal buay (, aus ) z y y z z z Shal ls ( s sua, s sua) y y z φ /# N s y y z z y z φ Oal b (, la, aus a) s N s a Gaussa Bas aa B s s as aus ' z ' wh z ' z as la z as a ls ( z ) '( z' ) ( z) ( z) > s Ba uau a ls h us Ba aa ' wh ' z z ' ( z) ' / z z z

2 QUTON SHTS FO C 47 Fbuay 7 z π z ( z) z z, x ( z) ( z) z π ( z, ) x π ( z) ( z) z π z z z z φ k (, z) kz ξ( z) ξ ( z) a ( z) z z F wll-lla ba a Os U(, ) U x( j ) U U x jk la wa Shal wa U ( ) x( jk) ' z π a j φ ω k k k ω k U x U a aula sl wh x by y a l wh << a << y x x y x, y s s a ula au a a l wh << π J y. π a a (sa a) B C a(s s ) Ba a ( y Λ ) s s Λ y la Os ( ha ) j (, ) { ω j } H (, ) { H ω } H jω jωε jωb jωµ H k H k H kk ω// k ω/ B

3 QUTON SHTS FO C 47 Fbuay 7 * S { H } / S B B H H x jk H ( ) H x ( jk ) k kxˆ ˆ x ky y kz zˆ ω k k k k ωµ H k H ωε µ µ µ π 77Ω H H ε ε ε la wa Fsl l a asss ( ) s s s w l w as T T T w w T T T buay s s s s s s T T buay T T ( T ) s s buay buay Fsl la ( al ) Bws al T ( < ) B a Slab au (, bh las, hkss a) K K a π φ π π Sl ax π/ α la s a F a a ax N T (s > s ) ak s π φ s φ a s s

4 QUTON SHTS FO C 47 Fbuay 7 4 T (s > s ) φ ak s π φ a s S x Oal Fb (, la, aus a) a N s ax la 4 Sl ax.45 β k b B F y - x K ( ) al s F sl (.5 6 a ) KB y x Ga x Oal Fb ( (), la, aus a) α, a, ( ) a ( ), a, la F axal N() Fb ss a ss α ak α ( z) α z GN (aa α) ax Gaussa α ( z) α l N / 4.4α B / z α a N N α k s σ σ ax σ.45 / aula σ.9 / α α ( ) /. 5σ / N α α 4 α ( ka)

5 QUTON SHTS FO C 47 Fbuay 7 5 B Z a T / 4σ NZ a T / σ T al lal / σ. 9 / ul S b GN b a /, 8,ax s σ a β β G w ω ω w h a w SYS TX TOT X σ σ σ al al σ X. C ha B C β ω ω ω ω ω ω ω C Fb Cul ss (laal, aula, lual s) 6 F 4 aal: S ul b C a s a a 8 aal: GN (aabl) ul b. π a T 85 a C π a aal: sl b ula: S ul b ula: sl b S, T x w π πw S, NG x

6 QUTON SHTS FO C 47 Fbuay 7 6 ual: S ul b a S a sa ( C ) ual: sl b z s S S w z, Oal sa T K ax ax ( ) 4 s ( ) ν ν ν ν ν α αs l T ν F π ν F δν N Jus KT N N l C ε ε q N N C C ε l x Ga -x s. ().44.66x.66x ~.59-.7x wh <x<.4 -x Ga x s y -y ().5-.7y.y wh <x<.47 a y.5x B B BN µ KT µ KT B B BN s x sx KT KT N b x x KT KT b x KT Φ al h lux Φ uu h lux x / l lux / l lux s N N

7 QUTON SHTS FO C 47 Fbuay 7 7 h Φ ( ) x h Oal w Ou C Cu lss S ( ) h x lss h Oal w Ou C lal w h Φ s ( N) ( ω ) ax B x h x.4 ( µ ) ( ) s ( ). 5 B ax as ls ρ N B N ρ ( h ) B N h ρ q x( z) ( h ) ( h ) B B 8π h x KT N N Bρ h N B 8π h ( ) h ρ ( h ) ( N N ) h h α al γ l ( N N ) h h B h as s sl B Λ u h B h Λ C h N h B B ± J h h ( ) s h J h x h s B h ( ) σ h h u hs ( ) ( ) h h α ax π al h s h h.4 ( µ ) ( ) ( x) x( α x) δ / α

8 QUTON SHTS FO C 47 Fbuay 7 8 h / h / h h h h h u h jω C j us ( C ) us s KT h x KT KT h Ns a s B N [ ( ) ] S s ( ) FB s ( ) ( ) F { } { } hu qualza h qualza ω C Tasa al SN ( ) s x s 4 h KTB B N B { } SN s s SN 4KT { } B { } B ( ) F π 4 (, ) B C C C s s SN 4KT ( s ) F ω C u 4KT F F s ( ) ( ) s h { } { } ( BC) { } { } ( BC) F C B B s h ( ) Oal Cs sa k Z u ( s( φ) ) φ π F SN NF SN h s G S u π

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