PHYSICS 230 – PROBLEM SET 6 1. Consider a potential of the form V ( x ) = λx 2 p . Using scaling arguments calculate E n using the WKB approximation, up to an unknown integral whose answer is a constant of order one. For p = 1 do the integral and compare your answers to the exact results for the Harmonic Oscillator. Consider the limit p → ∞ . Calculate the integral in this limit. Show that in this limit V ( x ) reduces to a well known exactly soluble problem. Compare the exact answers to your WKB answers. 2. Consider a potential of the following form: V ( x ) = x 2 + A, | x | < L V ( x ) = 0 , | x | > L Compute the exponential part of the tunneling time for a particle ini-
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