1
PHYS 342
Fall Semester 2011
Solutions: Homework No. 4
Due: October 14, 2011
1.
In an experiment, the speed of an electron is measured to be 6.0x10
5
m/s. Since all
measurements have an uncertainty associated with them, in this case say the
electron speed is only measured to an accuracy of
1.0x10
4
m/s.
This implies that
the uncertainty in the speed of the electron is therefore 2x10
4
m/s. According to
quantum mechanics, what is the size of the smallest region in space in which the
electron could be found?

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2
2.
Consider the wave form shown below
Assume the wave can be represented by the formula
By inspection, what are your best guesses for B, C,
1
and
2
? Assume
2
>
1
.
1
2
2
2
sin
sin
x
x
A
B
C
‐
3
‐
2
‐
1
0
1
2
3
0.00
0.01
0.02
0.03
0.04
0.05
0.06
Amplitude, A
x (in m)

3
3.
a) Write down the solution to the angular Schrödinger’s Equation for the m=+1,
ℓ
=1
quantum state of atomic hydrogen.
b)
Verify that the spherical harmonic Y
11
(
ϑ
,
φ
) you wrote in a) satisfies the angular
Schrödinger’s Equation

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