Physics 220
Homework #4
Spring 2016
Due Monday, April 25, 2015
Finite Well Problems
1.
Determine the odd solutions to the finite square well. Determine the energy of the single bound state with E
<
V
0
. Normalize your solutions in each region to determine the unknown coefficient A in each region. Plot your solution for
ψ
2
( x ) .
2.
Determine the normalization coefficients for the second energy state of the even solutions to the finite square well. That is, renormalize the solutions and determine B in each region for E solutions for ψ
2
3
. Plot your solution for ψ
( x ) from above and ψ
1
( x ) from class.
3
( x ) , along with the
3.
Griffith’s problem 2.40
4.
Griffith’s problem 2.47
Potential Barrier Problems
5.
Griffith’s P2.33
6.
Consider reflection from a step potential of height V
0
with E
>
V
0
but now with an infinitely high wall added at a distance a from the step as shown below. a.
What is ψ
( x ) in each region? b.
Show that the reflection coefficient at x
=
0 is R
=
1 . This is different than the previously derived reflection coefficient without the infinite wall? What is the physical reason that R
=
1 in this case? c.
Which part of the wave function represents a left moving particle at x ≤ 0 ?
Show that this part of the wave function is an eigenfunction of the momentum operator and calculate the eigenvalue. Is the total wave function for x
≤
0 an eigenfunction of the momentum operator?
E
V = 0
V(x)
V = V
0 x = 0 x = a x