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Homework #10
— PHYS 402 — Spring 2011
Deadline:
Wednesday, April 27, 2011, in class
Professor Victor Yakovenko
Oﬃce: 2115 Physics
Web page:
http://www2.physics.umd.edu/
~
yakovenk/teaching/
Textbook: David J. Griﬃths,
Introduction to Quantum Mechanics
2nd edition, Pearson Prentice Hall, 2005, ISBN 0131118927
Do not forget to write your name and the homework number!
Be sure to answer all additional questions asked in this assignment!
Total score is 38 points.
Ch. 8 The WKB Approximation
1. Problem 8.1, 8 points.
A “shelf” in the inﬁnite square well.
Use Eq. (8.16) to ﬁnd the allowed energies
E
n
.
2. Problem 8.4, 10 points.
Lifetimes of U
238
and Po
212
.
For the reference: Atomic unit is 1 u = 931 MeV/
c
2
.
The mass of
α
particle (He
4
) is
m
= 4
.
002602 u = 3727 MeV/
c
2
.
U
238
(
Z
= 92,
A
= 238,
m
= 238
.
050784 u) decays into Th
234
(
m
= 234
.
043593 u).
Po
212
(
Z
= 84,
A
= 212,
m
= 211
.
988842 u) decays into Pb
208
(
m
= 207
.
976627 u).
3. Triangular potential, 10 points.
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