Quiz5Sol - 1. Problem 1 a) y U=infinite y=L/4 U=0 x=L x x=0...

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1. Problem 1 a) y=L/4 x y U=infinite U=infinite U=infinite U=infinite U=0 U=0 U=0 U=0 x=L x=0 y= L/4 b) For the full detail see last week’s quiz. For these solutions I will use a shortcut. First we know Ψ( x, y )= ψ 1 ( x ) ψ 2 ( y ). Also ψ 1 ( x ) is given on the formula sheet, ψ 1 ( x )= q 2 L sin ( L x ) . To ±nd ψ 2 ( y ) we just tweak this answer a bit. The length of the box in this direction is L/ 2no t L . So± r s twerep laceLintheg ivenso lu t ionw i th L/ 2. Also our box now begins at L/ 4, not 0. To compensate we subtract L/ 4from y .Thu sou r answer is: ψ 2 ( y )= q 2 L/ 2 sin ± L/ 2 ( y + L/ 4) ² . So the wavefunctions are: Ψ( x, y )= 2 2 L sin ± n x π L x ² sin ³ 2 n y π L ( y + L/ 4) ´ (1 . 1) We can see that the normalization constant is 2 2 L . The corresponding probability densities are: P ( x, y )= | Ψ( x, y ) | 2 = 8 L 2 sin 2 ± n x π L x ² sin 2 ³ 2 n
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Quiz5Sol - 1. Problem 1 a) y U=infinite y=L/4 U=0 x=L x x=0...

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