PHYSICS 212 CHECK-OUT QUESTIONS
Laboratory 24: Energy Levels (Numerical)
1. The iterative numerical method is being used to calculate the wave function for
a potential , with
)(xψ
2
0xUU =10
0
=
U and a trial energy 2
=
E. Fill in the missing
values in the table below. Write your answers to three decimal places.
ψ( )
x
x
0
0.1
0.2
1 −0.200 −1.900
10−2
ψ ( ) ψ ( )xx
2. Consider the simple harmonic oscillator potential U = x2. A numerical integration of
Schrödinger's equation with two indicated values of the energy E gives the following
graphs of two different wave functions:
E = 4
ψ
(x)
x
E = 1
ψ
(x)
x
Of the following statements, circle the one that is TRUE.
a) There are no allowed energy levels in the range 1 ≤ E ≤ 4.
b) There is exactly 1 allowed energy level in the range 1 ≤ E ≤ 4.
c) There are exactly 2 allowed energy levels in the range 1 ≤ E ≤ 4.
d) There are more than 2 allowed energy levels in the range 1 ≤ E ≤ 4
e) It is impossible to tell how many allowed energy levels are in the range 1 ≤ E ≤ 4
from the given information.
