Review Questions
© Leon van Dommelen
To:
4.1 Wave Function for Multiple Particles
4
. Multiple-Particle Systems
Subsections
4
.
1
Wave Function for Multiple Particles
4
.
2
The Hydrogen Molecule
4
.
2
.
1
The Hamiltonian
4
.
2
.
2
Initial approximation to the lowest energy state
4
.
2
.
3
The probability density
4
.
2
.
4
States that share the electrons
4
.
2
.
5
Variational approximation of the ground state
4
.
2
.
6
Comparison with the exact ground state
4
.
3
Two-State Systems
4
.
4
Spin
4
.
5
Multiple-Particle Systems Including Spin
4
.
5
.
1
Wave function for a single particle with spin
4
.
5
.
2
Inner products including spin
4
.
5
.
3
Commutators including spin
4
.
5
.
4
Wave function for multiple particles with spin
4
.
5
.
5
Example: the hydrogen molecule
4
.
5
.
6
Triplet and singlet states
4
.
6
Identical Particles
4
.
7
Ways to Symmetrize the Wave Function
4
.
8
Matrix Formulation
4
.
9
Heavier Atoms [Descriptive]
4
.
9
.
1
The Hamiltonian eigenvalue problem
4
.
9
.
2
Approximate solution using separation of variables
4
.
9
.
3
Hydrogen and helium
4
.
9
.
4
Lithium to neon
4
.
9
.
5
Sodium to argon
4
.
9
.
6
Potassium to krypton
4
.
10
Pauli Repulsion [Descriptive]
4
.
11
Chemical Bonds [Descriptive]
4
.
11
.
1
Covalent sigma bonds
4
.
11
.
2
Covalent pi bonds
4
.
11
.
3
Polar covalent bonds and hydrogen bonds
4
.
11
.
4
Promotion and hybridization
4
.
11
.
5
Ionic bonds
4
.
11
.
6
Limitations of valence bond theory
To:
4.1 Wave Function for Multiple Particles
FAMU-FSU College of Engineering
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