equations.829 - m P z sin t W DM t =-qB 2 m L x 2 S x c o s...

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SOME BASIC EQUATIONS Some Spherical Harmonics: H = T + V = P 2 / 2 M + V ( R ) = | < | H | = i h | t H | = E | | u i i < u i | = 1 d | >< |=1 [ J x , J y ] = i h J z J 2 | jm = j ( j + 1) h 2 | jm J z | jm = m h | jm m = j , j - 1, j - 2,. ..., - j J ± = J x ± iJ y 2 = 1 r 2 r 2 r + 1 r 2 sin (sin ) + 1 r 2 sin 2 2 2 L z = h i L 2 = - h 2 { 2 2 + 1 tan + 1 sin 2 2 2 } Y l m ( , ) = N l m e im P l m ( ); P l m - associated Legendre functions cos Y l m = ( l + m + 1)( l - m + 1) (2 l + 1)(2 l + 3) Y l + 1 m + ( l + m )( l - m ) (2 l + 1)(2 l - 1) Y l - 1 m Y 0 0 = 1 4 Y 1 ± 1 = m 3 8 sin e ± i Y 1 0 = 3 4 cos Y 2 ± 1 = m 15 8 sin cos e ± i Y 2 0 = 5 16 (3cos 2 - 1) Y 2 ± 2 = 15 32 sin 2 e ± 2 i P x = h i x X = i h p x [ - h 2 2 m d 2 dr 2 + l ( l + 1) h 2 2 mr 2 + V ( r )] u k , l ( r ) = k 2 h 2 2 m u k , l ( r )
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APPROXIMATION METHODS kdx = ( n + 1/2) a b H ⟩≥ E 0 P tunn = exp - 2 ( x ) dx x 1 x 2 E n 2 = E n 0 + W nn + | W np | 2 E n 0 - E p 0 p n p |1 ⟩ = 1 E n 0 - E p 0 p | W | n ; p n H = H i 0 i = 1 N + e 2 r ij i < j H H i 0 + V i eff ( 29 i ; V i eff = j i | j ( j )| 2 r ij d j (1,2,3,. .. N ) = i i = 1 N ( i ) i h db n ( t ) dt = e iw nk t k W nk ( t ) b k ( t ) can be solved by successive approximation Γ = 2 h | W fi | 2 ( E ) d ( E ) = 2 2 (2 c ) 3 h V Γ = 2 h | W ' fi | 2 ( E ) d n + 1 a + n = ( n + 1) 1/2 n - 1 a n = n 1/2 W ( t ) 2245 - q m P z A z = - q m P z A 0 e i ( ky - t ) + A 0 e - i ( ky - t ) { } W DE ( t ) = qE
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Unformatted text preview: m P z sin t W DM ( t ) =-qB 2 m ( L x + 2 S x ) c o s t W QE ( t ) =-qE 2 mc ( YP z + ZP y )cos t A = h 2 ∑ 1/2 a A + a A [ ] 1 V A = e e i k • r b m = 〈 m (1) | i ( 0 ) 〉 P fi ( , t ) = | W fi | 2 4 h 2 sin 2-fi ( 29 t / 2 [ ]-fi ( 29 / 2 [ ] 2 S = 1 N ! P ∑ A = 1 N ! P ∑ (if ϖ =0, then remove "4" from denominator )...
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equations.829 - m P z sin t W DM t =-qB 2 m L x 2 S x c o s...

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