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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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This note was uploaded on 02/01/2011 for the course MATH 171 taught by Professor R during the Spring '09 term at Stanford.
 Spring '09
 R
 Approximation

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