Quantum Mechanics for Engineers 5.55 alpha
© 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
Example application 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
The basic Born-Oppenheimer approximation
9
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2
.
3
Going one better
9
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3
The Hartree-Fock Approximation
9
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3
.
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
.
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
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
.
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
.
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
.
10
Three-dimensional metals
10
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4
Covalent Materials
10
.
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
.
2
Occupied states and Brillouin zones
10
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6
Nearly-Free Electrons
10
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6
.
1
Energy changes due to a weak lattice potential
10
.
6
.
2
Discussion of the energy changes
10
.
7
Additional Points
10
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7
.
1
About ferromagnetism
10
.
7
.
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
.
8
Intro to the Second Law
11
.
9
The Reversible Ideal
11
.
10
Entropy
11
.
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
.
14
.
2
Fermions at low temperatures
11
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14
.
3
A generalized ideal gas law
11
.
14
.
4
The ideal gas
11
.
14
.
5
Blackbody radiation
11
.
14
.
6
The Debye model
11
.
15
Specific Heats
12
. Angular momentum
12
.
1
Introduction
12
.
2
The fundamental commutation relations
12
.
3
Ladders
12
.
4
Possible values of angular momentum
12
.
5
A warning about angular momentum
12
.
6
Triplet and singlet states
12
.
7
Clebsch-Gordan coefficients
12
.
8
Some important results
12
.
9
Momentum of partially filled shells
12
.
10
Pauli spin matrices
12
.
11
General spin matrices
12
.
12
The Relativistic Dirac Equation
13
. Electromagnetism
13
.
1
The Electromagnetic Hamiltonian
13
.
2
Maxwell’s Equations
13
.
3
Example Static Electromagnetic Fields
13
.
3
.
1
Point charge at the origin
13
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3
.
2
Dipoles
13
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3
.
3
Arbitrary charge distributions
13
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3
.
4
Solution of the Poisson equation
13
.
3
.
5
Currents
13
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3
.
6
Principle of the electric motor
13
.
4
Particles in Magnetic Fields
13
.
5
Stern-Gerlach Apparatus
13
.
6
Nuclear Magnetic Resonance
13
.
6
.
1
Description of the method
13
.
6
.
2
The Hamiltonian
13
.
6
.
3
The unperturbed system
13
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6
.
4
Effect of the perturbation
14
. Nuclei [Unfinished Draft]
14
.
1
Fundamental Concepts
14
.
2
The Simplest Nuclei
14
.
2
.
1
The proton
14
.
2
.
2
The neutron
14
.
2
.
3
The deuteron
14
.
2
.
4
Property summary
14
.
3
Modeling the Deuteron
14
.
4
Overview of Nuclei
14
.
5
Magic numbers
14
.
6
Radioactivity
14
.
6
.
1
Decay rate
14
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6
.
2
Other definitions
14
.
7
Mass and energy
14
.
8
Binding energy
14
.
9
Nucleon separation energies
14
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10
Liquid drop model
14
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10
.
1
Nuclear radius
14
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10
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2
von Weizsäcker formula
14
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10
.
3
Explanation of the formula
14
.
10
.
4
Accuracy of the formula
14
.
11
Alpha Decay
14
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11
.
1
Decay mechanism
14
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11
.
2
Comparison with data
14
.
11
.
3
Forbidden decays
14
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11
.
4
Why alpha decay?
14
.
12
Shell model
14
.
12
.
1
Average potential
14
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12
.
2
Spin-orbit interaction
14
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12
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3
Example occupation levels
14
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12
.
4
Shell model with pairing
14
.
12
.
5
Configuration mixing
14
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12
.
6
Shell model failures
14
.
13
Collective Structure
14
.
13
.
1
Classical liquid drop
14
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13
.
2
Nuclear vibrations
14
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13
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3
Nonspherical nuclei
14
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13
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4
Rotational bands
14
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13
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4
.
1
Basic notions in nuclear rotation
14
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13
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4
.
2
Basic rotational bands
14
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13
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4
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3
Bands with intrinsic spin one-half
14
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13
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4
.
4
Bands with intrinsic spin zero
14
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13
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4
.
5
Even-even nuclei
14
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13
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4
.
6
Nonaxial nuclei
14
.
14
Fission
14
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14
.
1
Basic concepts
14
.
14
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2
Some basic features
14
.
15
Spin Data
14
.
15
.
1
Even-even nuclei
14
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15
.
2
Odd mass number nuclei
14
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15
.
3
Odd-odd nuclei
14
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16
Parity Data
14
.
16
.
1
Even-even nuclei
14
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16
.
2
Odd mass number nuclei
14
.
16
.
3
Odd-odd nuclei
14
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16
.
4
Parity Summary
14
.
17
Electromagnetic Moments
14
.
17
.
1
Classical description
14
.
17
.
1
.
1
Magnetic dipole moment
14
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17
.
1
.
2
Electric quadrupole moment
14
.
17
.
2
Quantum description
14
.
17
.
2
.
1
Magnetic dipole moment
14
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17
.
2
.
2
Electric quadrupole moment
14
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17
.
2
.
3
Shell model values
14
.
17
.
2
.
4
Values for deformed nuclei
14
.
17
.
3
Magnetic moment data
14
.
17
.
4
Quadrupole moment data
14
.
18
Isospin
14
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18
.
1
Basic ideas
14
.
18
.
2
Heavier nuclei
14
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18
.
3
Additional points
14
.
18
.
4
Why does this work?
14
.
19
Beta decay
14
.
19
.
1
Energetics Data
14
.
19
.
2
Von Weizsäcker approximation
14
.
19
.
3
Kinetic Energies
14
.
19
.
4
Forbidden decays
14
.
19
.
4
.
1
Allowed decays
14
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19
.
4
.
2
Forbidden decays allowed
14
.
19
.
4
.
3
The energy effect
14
.
19
.
5
Data and Fermi theory
14
.
19
.
6
Parity violation
14
.
20
Gamma Decay
14
.
20
.
1
Energetics
14
.
20
.
2
Forbidden decays
14
.
20
.
3
Isomers
14
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20
.
4
Weisskopf estimates
14
.
20
.
5
Comparison with data
14
.
20
.
6
Cage-of-Faraday proposal
14
.
20
.
7
Internal conversion
Next:
9. Numerical Procedures
FAMU-FSU College of Engineering
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