Quantum Mechanics Solution Manual
© Leon van Dommelen
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4.1 The Harmonic Oscillator
4
. Single-Particle Systems
Subsections
4
.
1
The Harmonic Oscillator
4
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1
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1
The Hamiltonian
4
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1
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2
Solution using separation of variables
4
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1
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2
.
1
Solution harmb-a
4
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1
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2
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2
Solution harmb-b
4
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1
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2
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3
Solution harmb-c
4
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1
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2
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4
Solution harmb-d
4
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1
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3
Discussion of the eigenvalues
4
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1
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3
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1
Solution harmc-a
4
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1
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3
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2
Solution harmc-b
4
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1
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4
Discussion of the eigenfunctions
4
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1
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4
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1
Solution harmd-a
4
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1
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4
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2
Solution harmd-b
4
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1
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4
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3
Solution harmd-c
4
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1
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5
Degeneracy
4
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1
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5
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1
Solution harme-a
4
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1
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6
Noneigenstates
4
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2
Angular Momentum
4
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2
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1
Definition of angular momentum
4
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2
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2
Angular momentum in an arbitrary direction
4
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2
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2
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1
Solution angub-a
4
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2
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2
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2
Solution angub-b
4
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2
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2
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3
Solution angub-c
4
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2
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3
Square angular momentum
4
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2
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3
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1
Solution anguc-a
4
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2
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3
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2
Solution anguc-b
4
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2
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3
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3
Solution anguc-c
4
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2
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4
Angular momentum uncertainty
4
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3
The Hydrogen Atom
4
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3
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1
The Hamiltonian
4
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3
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2
Solution using separation of variables
4
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3
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2
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1
Solution hydb-a
4
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3
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2
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2
Solution hydb-b
4
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3
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2
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3
Solution hydb-c
4
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3
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3
Discussion of the eigenvalues
4
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3
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3
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1
Solution hydc-a
4
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3
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3
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2
Solution hydc-b
4
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3
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3
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3
Solution hydc-c
4
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3
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3
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4
Solution hydc-d
4
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3
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4
Discussion of the eigenfunctions
4
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3
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4
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1
Solution hydd-a
4
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3
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4
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2
Solution hydd-b
4
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3
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4
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3
Solution hydd-c
4
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4
Expectation Value and Standard Deviation
4
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4
.
1
Statistics of a die
4
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4
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1
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1
Solution esda-a
4
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4
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1
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2
Solution esda-b
4
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4
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1
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3
Solution esda-c
4
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4
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1
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4
Solution esda-d
4
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4
.
2
Statistics of quantum operators
4
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4
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2
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1
Solution esdb-a
4
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4
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2
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2
Solution esdb-b
4
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4
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3
Simplified expressions
4
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4
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3
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1
Solution esdb2-a
4
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4
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3
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2
Solution esdb2-b
4
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4
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4
Some examples
4
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5
The Commutator
4
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5
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1
Commuting operators
4
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5
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1
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1
Solution commutea-a
4
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5
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2
Noncommuting operators and their commutator
4
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5
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3
The Heisenberg uncertainty relationship
4
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5
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3
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1
Solution commutec-a
4
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5
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4
Commutator reference
4
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6
The Hydrogen Molecular Ion
4
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6
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1
The Hamiltonian
4
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6
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2
Energy when fully dissociated
4
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6
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3
Energy when closer together
4
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6
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4
States that share the electron
4
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6
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5
Comparative energies of the states
4
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6
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6
Variational approximation of the ground state
4
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6
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6
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1
Solution hione-a
4
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6
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7
Comparison with the exact ground state
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4.1 The Harmonic Oscillator
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