Ciro Santilli
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Non-relativistic quantum mechanics
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97
The first
quantum mechanics
theories developed.
Their most popular formulation has been the
Schrödinger equation
.
Table of contents
5k
97
Schrödinger equation
link
Non-relativistic quantum mechanics
5k
91
Time-independent Schrödinger equation
link
Schrödinger equation
603
1
Solving the Schrodinger equation with the time-independent Schrödinger equation
link
Time-independent Schrödinger equation
500
Derivation of the Schrodinger equation
link
Schrödinger equation
133
1
Why are complex numbers used in the Schrodinger equation?
link
Derivation of the Schrodinger equation
71
Schrodinger equation Hamiltonian
link
Schrödinger equation
The Schrodinger equation Hamiltonian has to be Hermitian
link
Schrödinger equation
15
Solutions of the Schrodinger equation
link
Schrödinger equation
3k
63
Schrödinger equation simulations
link
Solutions of the Schrodinger equation
233
1
Why it is hard to simulate quantum systems?
link
Schrödinger equation simulations
30
Schrödinger equation for a one dimensional particle
link
Solutions of the Schrodinger equation
60
Schrödinger equation for a free one dimensional particle
link
Solutions of the Schrodinger equation
150
2
Plane wave function
link
Schrödinger equation for a free one dimensional particle
68
Time-independent Schrödinger equation for a free one dimensional particle
link
Schrödinger equation for a free one dimensional particle
30
Particle in a box
link
Solutions of the Schrodinger equation
Quantum harmonic oscillator
link
Solutions of the Schrodinger equation
168
4
Quantum LC circuit
link
Quantum harmonic oscillator
13
Hermite polynomials
link
Quantum harmonic oscillator
35
1
Hermite functions
link
Hermite polynomials
5
Ladder operator
link
Quantum harmonic oscillator
39
Quantum tunnelling
link
Solutions of the Schrodinger equation
22
Schrödinger equation solution for the hydrogen atom
link
Solutions of the Schrodinger equation
612
11
Atomic orbital
link
Schrödinger equation solution for the hydrogen atom
48
Quantum number
link
Schrödinger equation solution for the hydrogen atom
463
9
Principal quantum number (n)
link
Quantum number
50
Azimuthal quantum number (l)
link
Quantum number
29
4
s-orbital
link
Azimuthal quantum number
p-orbital
link
Azimuthal quantum number
d-orbital
link
Azimuthal quantum number
f-orbital
link
Azimuthal quantum number
Magnetic quantum number (
m
l
)
link
Quantum number
157
Spin quantum number (
m
s
)
link
Quantum number
49
1
Spectroscopic notation
link
Spin quantum number
49
Solutions for the Schrodinger equation with multiple particles
link
Solutions of the Schrodinger equation
2k
34
Separable state (Product state)
link
Solutions for the Schrodinger equation with multiple particles
Solutions of the Schrodinger equation for two electrons
link
Solutions for the Schrodinger equation with multiple particles
134
Orbital approximation
link
Solutions for the Schrodinger equation with multiple particles
7
Schrödinger equation solution for the helium atom
link
Solutions for the Schrodinger equation with multiple particles
60
Hartree-Fock method
link
Solutions for the Schrodinger equation with multiple particles
732
12
Hartree-Fock method for the helium atom
link
Hartree-Fock method
Why do multiple electrons occupy the same orbital if electrons repel each other?
link
Hartree-Fock method
55
Aufbau principle
link
Hartree-Fock method
677
9
Electron configuration
link
Aufbau principle
Electron configuration notation (
1
s
2
2
s
2
2
p
6
, 1s2 2s2 2p6)
link
Aufbau principle
15
Why does 2s have less energy than 1s if they have the same principal quantum number?
link
Aufbau principle
73
Madelung energy ordering rule
link
Aufbau principle
139
1
Exception to the Madelung energy ordering rule
link
Madelung energy ordering rule
40
Term symbol (
2
S
1
/
2
,
2
P
1
/
2
,
2
P
3
/
2
)
link
Aufbau principle
423
3
Hund's rules (1927)
link
Term symbol
115
2
Hund's first rule
link
Hund's rules
18
Hund's second rule
link
Hund's rules
Term symbols for carbon ground state
link
Solutions for the Schrodinger equation with multiple particles
731
Schrödinger equation solution for molecule
link
Solutions for the Schrodinger equation with multiple particles
151
15
Schrödinger equation solution for the hydrogen molecule
link
Schrödinger equation solution for molecule
40
Chemical bond
link
Schrödinger equation solution for molecule
111
13
Molecule
link
Chemical bond
111
5
Isomer
link
Molecule
111
4
Cis-trans isomerism
link
Isomer
14
Enantiomer
link
Isomer
30
Polymorphism (materials science)
link
Isomer
13
Stereochemistry
link
Isomer
30
Covalent bond
link
Chemical bond
4
Sigma bond
link
Covalent bond
Pi bond
link
Covalent bond
2
Double bond
link
Pi bond
Triple bond
link
Pi bond
Ionic bond
link
Chemical bond
Octet rule
link
Chemical bond
Two-state quantum system
link
Solutions of the Schrodinger equation
42
2
Bloch sphere
link
Two-state quantum system
22
Pauli matrix
link
Two-state quantum system
1
Born-Oppenheimer approximation
link
Schrödinger equation
Uncertainty principle
link
Schrödinger equation
842
10
Position and momentum space
link
Uncertainty principle
296
4
Position representation
link
Position and momentum space
72
Position operator
link
Position and momentum space
25
Momentum operator
link
Position and momentum space
61
Squeezed coherent state
link
Position and momentum space
Energy operator
link
Uncertainty principle
24
1
Time-energy uncertainty principle
link
Energy operator
14
Angular momentum operator (Quantum angular momentum)
link
Uncertainty principle
151
1
Total angular momentum operator
link
Angular momentum operator
2
Complementarity (physics)
link
Uncertainty principle
Conservation laws in Schrodinger equations
link
Schrödinger equation
64
2
Conservation of the square amplitude in the Schrodinger equation
link
Conservation laws in Schrodinger equations
48
1
Probability current
link
Conservation of the square amplitude in the Schrodinger equation
Wave function (
ψ
)
link
Schrödinger equation
160
5
Matter wave (1923, de Broglie hypothesis)
link
Wave function
74
4
Electron diffraction experiment
link
Matter wave
2
Diffraction of Cathode Rays by a Thin Film by Thomson and Reid (1927)
link
Electron diffraction experiment
Davisson-Germer experiment (1927)
link
Electron diffraction experiment
de Broglie relations
link
Matter wave
74
Equivalent alternatives to the Schrodinger equation
link
Non-relativistic quantum mechanics
152
4
Matrix mechanics (1925)
link
Equivalent alternatives to the Schrodinger equation
149
2
Quantum mechanical re-interpretation of kinematic and mechanical relations by Heisenberg (1925) (Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen)
link
Matrix mechanics
24
Heisenberg picture
link
Matrix mechanics
11
De Broglie-Bohm theory
link
Equivalent alternatives to the Schrodinger equation
3
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