ch38-p062

# ch38-p062 - 62(a The wave function is now given by x t = 0...

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(b) Consider two plane matter waves, each with the same amplitude ψ 0 2 / and traveling in opposite directions along the x axis. The combined wave Ψ is a standing wave: () 00 0 0 (,) ( ) ( 2 c o s ) . ik x t i k x i k x it x te e e e e k x e ω ωω ψψ −− + Ψ= + = + = Thus, the squared amplitude of the matter wave is |( , ) | ( c o s) ( ) , Ψ xt kx e kx 2 0 2 2 0 2 22 1 == + cos2 which is shown below. (c) We set Ψ ,c o s b g b g 2 0 2 21 2 0 =+ = to obtain cos(2 kx ) = –1. This gives ( ) 2 2 1 0 , 1 , 2 , 3 , kx n n π ⎛⎞ + , = ⎜⎟ λ ⎝⎠ We solve for x : xn 1 4 bg λ . 62. (a) The wave function is now given by Ψ ( ) . e e e e e i k x i k x = + + Thus, 2 2 2 2 000 2 2 2 0 , ) | ( ) | (cos sin ) (cos sin ) | 4 (cos ) 2 (1 cos2 ). i k x i k x i k x i k x i k x i k x x t eee e ee kx i kx kx i kx kx kx ψψψ

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ch38-p062 - 62(a The wave function is now given by x t = 0...

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