HW5 - ECE 162A HW 5 Due Tuesday, Nov. 13, 2007 1. Separable...

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ECE 162A HW 5 Due Tuesday, Nov. 13, 2007 1. Separable Potentials (a) What is the condition on the 3-D potential V(x,y,z) for the SWE to be separable into three equations in the three components x, y and z? (b) Classify the following potentials into separable and inseparable. Give reasons. If separable, write it out in the form that answers question 1(a). (i) V(x,y,z) = 0, if 0 < x, y, z (all three) < L = infinity otherwise. (ii) V(x,y,z) = 0, if 0 < x, y, z (all three) < L = V 0 otherwise. (V 0 is a finite constant) 2. Solution of the Time-dependent Schrodinger Equation Consider the set ‘S’ of all functions of ‘x’ (real) which are 0 everywhere except possibly in the region 0 < x < L. Of this set, consider the member: f(x) = 1/sqrt(a), for (L-a)/2 < x < (L+a)/2 = 0 elsewhere. ‘a’ is a constant less than ‘L’. (a) Sketch f(x) on paper. (b) Choose an infinite set of functions to expand f(x) as a series in. One restriction on this set is that all members belong to ‘S’. One set comes
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HW5 - ECE 162A HW 5 Due Tuesday, Nov. 13, 2007 1. Separable...

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