Ciro Santilli
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Non-relativistic quantum mechanics
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↑ parent "Quantum mechanics"
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24
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36
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⇓ toc
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↑ parent "Quantum mechanics"
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24
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36
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The first
quantum mechanics
theories developed.
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Their most popular formulation has been the
Schrodinger equation
.
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Table of contents
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1. Schrodinger equation
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153
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35
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↑ parent "Non-relativistic quantum mechanics"
1.1. Time-independent Schrodinger equation
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207
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1.2. Derivation of the Schrodinger equation
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87
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1
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125
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↑ parent "Schrodinger equation"
1.2.1. Why are complex numbers used in the Schrodinger equation?
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38
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↑ parent "Derivation of the Schrodinger equation"
1.3. Solutions of the Schrodinger equation
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31
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19
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976
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↑ parent "Schrodinger equation"
1.3.1. Schrodinger equation simulations
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252
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1
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313
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↑ parent "Solutions of the Schrodinger equation"
1.3.1.1. Why it is hard to simulate quantum systems?
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61
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1.3.2. Schrodinger equation solution for a free particle
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1.3.3. Particle in a box
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↑ parent "Solutions of the Schrodinger equation"
1.3.4. Quantum harmonic oscillator
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0
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1
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28
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↑ parent "Solutions of the Schrodinger equation"
1.3.4.1. Hermite polynomials
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28
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↑ parent "Quantum harmonic oscillator"
1.3.5. Quantum tunnelling
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34
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1.3.6. Schrodinger equation solution for the hydrogen atom
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81
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↑ parent "Solutions of the Schrodinger equation"
1.3.7. Solutions for the Schrodinger equation with multiple particles
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19
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7
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404
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↑ parent "Solutions of the Schrodinger equation"
1.3.7.1. Solutions of the Schrodinger equation for two electrons
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155
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↑ parent "Solutions for the Schrodinger equation with multiple particles"
1.3.7.2. Schrodinger equation solution for the helium atom
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91
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4
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179
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↑ parent "Solutions for the Schrodinger equation with multiple particles"
1.3.7.2.1. Hartree-Fock method
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0
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3
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88
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↑ parent "Schrodinger equation solution for the helium atom"
1.3.7.2.1.1. Hartree-Fock method for the helium atom
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1.3.7.2.1.2. Why do multiple electrons occupy the same orbital if electrons repel each other?
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57
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↑ parent "Hartree-Fock method"
1.3.7.2.1.3. Aufbau principle
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31
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↑ parent "Hartree-Fock method"
1.3.7.3. Schrodinger equation solution for the hydrogen molecule
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51
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↑ parent "Solutions for the Schrodinger equation with multiple particles"
1.3.8. Two-state quantum system
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50
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2
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85
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↑ parent "Solutions of the Schrodinger equation"
1.3.8.1. Bloch sphere
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35
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↑ parent "Two-state quantum system"
1.3.8.2. Pauli matrix
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↑ parent "Two-state quantum system"
1.4. Born-Oppenheimer approximation
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↑ parent "Schrodinger equation"
1.5. Uncertainty principle
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251
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7
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504
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1.5.1. Position and momentum space
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103
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3
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205
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↑ parent "Uncertainty principle"
1.5.1.1. Position representation
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18
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↑ parent "Position and momentum space"
1.5.1.2. Position operator
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36
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↑ parent "Position and momentum space"
1.5.1.3. Momentum operator
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48
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↑ parent "Position and momentum space"
1.5.2. Energy operator
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22
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1
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48
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↑ parent "Uncertainty principle"
1.5.2.1. Time-energy uncertainty principle
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26
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↑ parent "Energy operator"
1.5.3. Complementarity (physics)
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↑ parent "Uncertainty principle"
1.6. Conservation laws in Schrodinger equations
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17
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63
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↑ parent "Schrodinger equation"
1.6.1. Conservation of the square amplitude in the Schrodinger equation
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46
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↑ parent "Conservation laws in Schrodinger equations"
1.7. Wave function (
ψ
)
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104
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↑ parent "Schrodinger equation"
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Incoming links
Lecture 1
Quantum mechanics