Materials Science and Engineering 451 Prof. Mark C. Hersam, Fall 2013

QUANTUM MECHANICAL FOUNDATIONS OF MATERIALS SCIENCE

Homework #1

Due: Friday, October 11, 2013

1.) (15 points) Griffiths, Problem 1.7 2.) (15 points) Griffiths, Problem 1.18 3.) (25 points) Griffiths, Problem 2.5

For this problem, the following equations may be helpful:

1sin sin cos cos

2A B A B A B

2

22

sin 2 cos 2sin

4 4 8

x x ax axx ax dx

a a

2

cos sincos

ax x axx ax dx

a a

4.) (10 points) Griffiths, Problem 2.14

For this problem, the following equation may be helpful:

2axe dxa

5.) (35 points) Griffiths, Problem 2.22

For this problem, the following equations may be helpful:

If Re{u} > 0, uvvxux e

udxee 4/22

; 22

3/ 22uxx e dx

u