Quantum Mechanics Solution Manual
© Leon van Dommelen
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5.1 Wave Function for Multiple Particles
5
. Multiple-Particle Systems
Subsections
5
.
1
Wave Function for Multiple Particles
5
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1
.
1
Solution complex-a
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1
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2
Solution complex-b
5
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2
The Hydrogen Molecule
5
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2
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1
The Hamiltonian
5
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2
.
1
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1
Solution hmola-a
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2
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1
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2
Solution hmola-b
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2
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2
Initial approximation to the lowest energy state
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2
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2
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1
Solution hmolb-a
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2
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2
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2
Solution hmolb-b
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2
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3
The probability density
5
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2
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3
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1
Solution hmolc-a
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2
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4
States that share the electrons
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2
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4
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1
Solution hmold-a
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2
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4
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2
Solution hmold-b
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2
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5
Variational approximation of the ground state
5
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2
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6
Comparison with the exact ground state
5
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3
Two-State Systems
5
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3
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1
Solution 2state-a
5
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3
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2
Solution 2state-b
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4
Spin
5
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4
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1
Solution spin-a
5
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4
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2
Solution spin-b
5
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5
Multiple-Particle Systems Including Spin
5
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5
.
1
Wave function for a single particle with spin
5
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5
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1
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1
Solution complexsa-a
5
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5
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2
Inner products including spin
5
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5
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2
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1
Solution complexsai-a
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5
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2
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2
Solution complexsai-b
5
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5
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3
Commutators including spin
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5
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3
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1
Solution complexsac-a
5
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5
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4
Wave function for multiple particles with spin
5
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5
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4
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1
Solution complexsb-a
5
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5
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4
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2
Solution complexsb-b
5
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5
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5
Example: the hydrogen molecule
5
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5
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5
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1
Solution complexsc-a
5
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5
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6
Triplet and singlet states
5
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5
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6
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1
Solution complexse-a
5
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6
Identical Particles
5
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6
.
1
Solution ident-a
5
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6
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2
Solution ident-b
5
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7
Ways to Symmetrize the Wave Function
5
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7
.
1
Solution symways-a
5
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7
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2
Solution symways-b
5
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8
Matrix Formulation
5
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8
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1
Solution matfor-a
5
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8
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2
Solution matfor-b
5
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9
Heavier Atoms
5
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9
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1
The Hamiltonian eigenvalue problem
5
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9
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2
Approximate solution using separation of variables
5
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9
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3
Hydrogen and helium
5
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9
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4
Lithium to neon
5
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9
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5
Sodium to argon
5
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9
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6
Potassium to krypton
5
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9
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7
Full periodic table
5
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10
Pauli Repulsion
5
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11
Chemical Bonds
5
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11
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1
Covalent sigma bonds
5
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11
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2
Covalent pi bonds
5
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11
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3
Polar covalent bonds and hydrogen bonds
5
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11
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4
Promotion and hybridization
5
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11
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5
Ionic bonds
5
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11
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6
Limitations of valence bond theory
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5.1 Wave Function for Multiple Particles
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