Quantum Mechanics for Engineers
© Leon van Dommelen
Next:
9. Numerical Procedures
III
. Gateway Topics
Subsections
9
. Numerical Procedures
9
.
1
The Variational Method
9
.
1
.
1
Basic variational statement
9
.
1
.
2
Differential form of the statement
9
.
1
.
3
Using Lagrangian multipliers
9
.
2
The Born-Oppenheimer Approximation
9
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2
.
1
The Hamiltonian
9
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2
.
2
Basic Born-Oppenheimer approximation
9
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2
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3
Going one better
9
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3
The Hartree-Fock Approximation
9
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3
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1
Wave function approximation
9
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3
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2
The Hamiltonian
9
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3
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3
The expectation value of energy
9
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3
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4
The canonical Hartree-Fock equations
9
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3
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5
Additional points
9
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3
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5
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1
Meaning of the orbital energies
9
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3
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5
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2
Asymptotic behavior
9
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3
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5
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3
Hartree-Fock limit
9
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3
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5
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4
Correlation energy
9
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3
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5
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5
Configuration interaction
10
. Solids
10
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1
Molecular Solids
10
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2
Ionic Solids
10
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3
Metals
10
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3
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1
Lithium
10
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3
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2
One-dimensional crystals
10
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3
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3
Wave functions of one-dimensional crystals
10
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3
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4
Analysis of the wave functions
10
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3
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5
Floquet (Bloch) theory
10
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3
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6
Fourier analysis
10
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3
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7
The reciprocal lattice
10
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3
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8
The energy levels
10
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3
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9
Merging and splitting bands
10
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3
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10
Three-dimensional metals
10
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4
Covalent Materials
10
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5
Free-Electron Gas
10
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5
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1
Lattice for the free electrons
10
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5
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2
Occupied states and Brillouin zones
10
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6
Nearly-Free Electrons
10
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6
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1
Energy changes due to a weak lattice potential
10
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6
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2
Discussion of the energy changes
10
.
7
Additional Points
10
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7
.
1
About ferromagnetism
10
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7
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2
X-ray diffraction
11
. Basic and Quantum Thermodynamics
11
.
1
Temperature
11
.
2
Single-Particle versus System States
11
.
3
How Many System Eigenfunctions?
11
.
4
Particle-Energy Distribution Functions
11
.
5
The Canonical Probability Distribution
11
.
6
Low Temperature Behavior
11
.
7
The Basic Thermodynamic Variables
11
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8
Intro to the Second Law
11
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9
The Reversible Ideal
11
.
10
Entropy
11
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11
The Big Lie of Distinguishable Particles
11
.
12
The New Variables
11
.
13
Microscopic Meaning of the Variables
11
.
14
Application to Particles in a Box
11
.
14
.
1
Bose-Einstein condensation
11
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14
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2
Fermions at low temperatures
11
.
14
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3
A generalized ideal gas law
11
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14
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4
The ideal gas
11
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14
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5
Blackbody radiation
11
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14
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6
The Debye model
11
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15
Specific Heats
12
. Angular momentum
12
.
1
Introduction
12
.
2
The fundamental commutation relations
12
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3
Ladders
12
.
4
Possible values of angular momentum
12
.
5
A warning about angular momentum
12
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6
Triplet and singlet states
12
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7
Clebsch-Gordan coefficients
12
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8
Some important results
12
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9
Momentum of partially filled shells
12
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10
Pauli spin matrices
12
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11
General spin matrices
12
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12
The Relativistic Dirac Equation
13
. Electromagnetism
13
.
1
The Electromagnetic Hamiltonian
13
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2
Maxwell’s Equations
13
.
3
Example Static Electromagnetic Fields
13
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3
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1
Point charge at the origin
13
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3
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2
Dipoles
13
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3
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3
Arbitrary charge distributions
13
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3
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4
Solution of the Poisson equation
13
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3
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5
Currents
13
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3
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6
Principle of the electric motor
13
.
4
Particles in Magnetic Fields
13
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5
Stern-Gerlach Apparatus
13
.
6
Nuclear Magnetic Resonance
13
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6
.
1
Description of the method
13
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6
.
2
The Hamiltonian
13
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6
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3
The unperturbed system
13
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6
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4
Effect of the perturbation
14
. Nuclei [Unfinished Draft]
14
.
1
Fundamental Concepts
14
.
2
Draft: The Simplest Nuclei
14
.
2
.
1
Draft: The proton
14
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2
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2
Draft: The neutron
14
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2
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3
Draft: The deuteron
14
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2
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4
Draft: Property summary
14
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3
Draft: Overview of Nuclei
14
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4
Draft: Magic numbers
14
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5
Draft: Radioactivity
14
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5
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1
Draft: Half-life and decay rate
14
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5
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2
Draft: More than one decay process
14
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5
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3
Draft: Other definitions
14
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6
Draft: Mass and energy
14
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7
Draft: Binding energy
14
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8
Draft: Nucleon separation energies
14
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9
Draft: Modeling the Deuteron
14
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10
Draft: Liquid drop model
14
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10
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1
Draft: Nuclear radius
14
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10
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2
Draft: von Weizsäcker formula
14
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10
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3
Draft: Explanation of the formula
14
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10
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4
Draft: Accuracy of the formula
14
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11
Draft: Alpha Decay
14
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11
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1
Draft: Decay mechanism
14
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11
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2
Draft: Comparison with data
14
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11
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3
Draft: Forbidden decays
14
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11
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4
Draft: Why alpha decay?
14
.
12
Draft: Shell model
14
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12
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1
Draft: Average potential
14
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12
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2
Draft: Spin-orbit interaction
14
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12
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3
Draft: Example occupation levels
14
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12
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4
Draft: Shell model with pairing
14
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12
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5
Draft: Configuration mixing
14
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12
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6
Draft: Shell model failures
14
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13
Draft: Collective Structure
14
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13
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1
Draft: Classical liquid drop
14
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13
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2
Draft: Nuclear vibrations
14
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13
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3
Draft: Nonspherical nuclei
14
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13
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4
Draft: Rotational bands
14
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13
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4
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1
Draft: Basic notions in nuclear rotation
14
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13
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4
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2
Draft: Basic rotational bands
14
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13
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4
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3
Draft: Bands with intrinsic spin one-half
14
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13
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4
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4
Draft: Bands with intrinsic spin zero
14
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13
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4
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5
Draft: Even-even nuclei
14
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13
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4
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6
Draft: Nonaxial nuclei
14
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14
Draft: Fission
14
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14
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1
Draft: Basic concepts
14
.
14
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2
Draft: Some basic features
14
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15
Draft: Spin Data
14
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15
.
1
Draft: Even-even nuclei
14
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15
.
2
Draft: Odd mass number nuclei
14
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15
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3
Draft: Odd-odd nuclei
14
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16
Draft: Parity Data
14
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16
.
1
Draft: Even-even nuclei
14
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16
.
2
Draft: Odd mass number nuclei
14
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16
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3
Draft: Odd-odd nuclei
14
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16
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4
Draft: Parity Summary
14
.
17
Draft: Electromagnetic Moments
14
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17
.
1
Draft: Classical description
14
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17
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1
.
1
Draft: Magnetic dipole moment
14
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17
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1
.
2
Draft: Electric quadrupole moment
14
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17
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2
Draft: Quantum description
14
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17
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2
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1
Draft: Magnetic dipole moment
14
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17
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2
.
2
Draft: Electric quadrupole moment
14
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17
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2
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3
Draft: Shell model values
14
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17
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2
.
4
Draft: Values for deformed nuclei
14
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17
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3
Draft: Magnetic moment data
14
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17
.
4
Draft: Quadrupole moment data
14
.
18
Draft: Isospin
14
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18
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1
Draft: Basic ideas
14
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18
.
2
Draft: Heavier nuclei
14
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18
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3
Draft: Additional points
14
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18
.
4
Draft: Why does this work?
14
.
19
Draft: Beta decay
14
.
19
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1
Draft: Introduction
14
.
19
.
2
Draft: Energetics Data
14
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19
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3
Draft: Beta decay and magic numbers
14
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19
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4
Draft: Von Weizsäcker approximation
14
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19
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5
Draft: Kinetic Energies
14
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19
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6
Draft: Forbidden decays
14
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19
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6
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1
Draft: Allowed decays
14
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19
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6
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2
Draft: Forbidden decays allowed
14
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19
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6
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3
Draft: The energy effect
14
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19
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7
Draft: Data and Fermi theory
14
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19
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8
Draft: Parity violation
14
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20
Draft: Gamma Decay
14
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20
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1
Draft: Energetics
14
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20
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2
Draft: Forbidden decays
14
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20
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3
Draft: Isomers
14
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20
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4
Draft: Weisskopf estimates
14
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20
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5
Draft: Comparison with data
14
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20
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6
Draft: Internal conversion
Next:
9. Numerical Procedures
FAMU-FSU College of Engineering
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