HW Set #5
Due 10/12/10 (at the beginning of class)
Problems from Chapter 5
2, 4, 6, 10, 14, 16, 18, 20, 24 32, 34, 54, 56
(note soon problems require working some previous odd numbered problems)
Other problems.
1.
There is another quantum mechanical problem similar to the particle in a box, that is
the particle on a ring (fixed radius in 2d).
This problem is one dimensional as the only
variable is the angle around the ring.
ˆ
H
=
−
2
2
m
∇
2
where m is the mass.
The 2
nd
derivative depends on the value of the radius and the angle
such that the Hamiltonian is
ˆ
H
=
−
2
2
mr
2
∂
2
∂φ
2
Given that the solutions to this problem are
ψ
n
(
φ
)
=
1
π
exp(
in
)
where n= 0,±1,±2,….
What are the energies.
And yes the wavefunctions are complex where i = sqrt(1)
2.
What is the most probable radius for the 1s Hatom wavefunction?
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 Spring '07
 campion
 Energy, Zeff, Bohr radii, Hatom wavefunction

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