PHY251 Homework Set 6
Reading:
Chapter 6 and 7
Homework:
Chapter 6, Question 9 Problems 2, 9,18 Chapter 7, Problems 16,20
Hints and Solutions
Question VI.9
Suppose you have a box a few centimeters wide and an electron with the energy of a few electron
volts (i.e. of the same order of magnitude as an electron in a Bohr orbit). In what range would the
n
values for the electron in the box lie?
Hints:
No hints
Solution:
No Solution yet
Problem VI.2
Consider the normalized wave function of the form
ψ
(
x
) =
C
exp{

x
²
/
2
a
²
). Calculate the expectation
values
(a)
⟨
x
⟩
,
(b)
⟨
x
²
⟩
,
(c)
⟨
p
⟩
, and
(d)
⟨
p
²
⟩
for this wave function. Give a physical justification of
your results for (a) and (c).
Hints:
The value of the normalization constant
C
should not matter. Use the definition of the
expectation value, and the operator identity:
p
= 
ih
(
∂
/
∂
x
) .
Solution:
No Solution yet
Problem VI.9
A beam of photons in a range of wavelengths
λ
= 9.0 ± 1.0 nm impinges on an electron in an
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 Spring '01
 Rijssenbeek
 Physics, Energy, Work

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