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ECE 162A
HW 5
Due Tuesday, Nov. 13, 2007
1.
Separable Potentials
(a) What is the condition on the 3D 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 Timedependent 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 (La)/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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 Fall '07
 johnbowers

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