Homework 4
Mechanics 701, Fall 2009
Due: Friday, September 11
1
Problem 2.12
The term generalized mechanics came to designate a variety of classical mechanics in which
the Lagrangian contains the derivatives of qi higher than the rst. Problems for which x

Gasiorowicz 3rd edition
P4-8.
Mar 4, 2008
Consider the potential shown in the figure
V
E
V(x)
x
R
with
h 2 l (l + 1)
V(x ) =
2mx 2
x>R
Estimate the lifetime of a particle of energy E in this potential. (The outside potential
represents a centrifugal barri

Start with a triangular well problem. Change from linear potential to exponential.
Potential with exponential slope (e^x) bound at one side by infinite barier.
_
Describe the potential and write the Schrodinger equation.
For x > 0 we have a potential of V

Original Problem:
*1&2
A particle of energy greater than the minimum potential comes from the left and hits the following step
potential. Write wave function. Find R and T. Find E where R = T.
SOLUTION:
REGION I:
Psi1(x) = Ae^ikx + Be^-ikx
Psi2(x)=CeiKx +

Original Problem:
*1&2
A particle of energy greater than the minimum potential comes from the left and hits the following step
potential. Write wave function. Find R and T. Find E where R = T.
Next (problem I found interesting, related to 0 and 1&2):
Simi