PHYSICS 137B Midterm: physics137B-sp2017-mt2-Mueller-soln
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1. (a) for a potential with two sloped walls, we have the following quantization con- dition (see gri ths pg 332). Z x+ x p2m(e v (x))dx = (n 1/2) m 2 , are the classical turning points. Using the proved integral with b = 1/x2: If we substitute x+ =q 2e m 2 , we nd: We see wkb gives the exact energies for a sho is this case. (don"t let the. 1/2 bother you, its just a statement that we begin indexing our solutions at n = 1 instead of n = 0. (b) at energies where the turning point is x = |a|, the quantization condition be- comes: The integral has exactly the same form as that in part a (but with di erent bounds). We can simplify ur result if we take x0 >> a, (note there is a typo in the problem). Note to rst order, arcsin( ) and 1 = 1.
