Review Questions
© Leon van Dommelen
To:
3.1 Angular Momentum
3
. Single-Particle Systems
Subsections
3
.
1
Angular Momentum
3
.
1
.
1
Definition of angular momentum
3
.
1
.
2
Angular momentum in an arbitrary direction
3
.
1
.
3
Square angular momentum
3
.
1
.
4
Angular momentum uncertainty
3
.
2
The Hydrogen Atom
3
.
2
.
1
The Hamiltonian
3
.
2
.
2
Solution using separation of variables
3
.
2
.
3
Discussion of the eigenvalues
3
.
2
.
4
Discussion of the eigenfunctions
3
.
3
Expectation Value and Standard Deviation
3
.
3
.
1
Statistics of a die
3
.
3
.
2
Statistics of quantum operators
3
.
3
.
3
Simplified expressions
3
.
3
.
4
Some examples
3
.
4
The Commutator
3
.
4
.
1
Commuting operators
3
.
4
.
2
Noncommuting operators and their commutator
3
.
4
.
3
The Heisenberg uncertainty relationship
3
.
4
.
4
Commutator reference [Reference]
3
.
5
The Hydrogen Molecular Ion
3
.
5
.
1
The Hamiltonian
3
.
5
.
2
Energy when fully dissociated
3
.
5
.
3
Energy when closer together
3
.
5
.
4
States that share the electron
3
.
5
.
5
Comparative energies of the states
3
.
5
.
6
Variational approximation of the ground state
3
.
5
.
7
Comparison with the exact ground state
To:
3.1 Angular Momentum
FAMU-FSU College of Engineering
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