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Solutions of the Schrodinger equation
...
Natural science
Physics
Particle physics
Quantum mechanics
Non-relativistic quantum mechanics
Schrödinger equation
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words: 3k
articles: 65
en.wikipedia.org/wiki/List_of_quantum-mechanical_systems_with_analytical_solutions
As always, the best way to get some intuition about an equation is to solve it for some simple cases, so let's give that a try with different fixed potentials.
Table of contents
3k
65
Schrödinger equation simulations
Solutions of the Schrodinger equation
233
1
Why it is hard to simulate quantum systems?
Schrödinger equation simulations
30
Schrödinger equation for a one dimensional particle
Solutions of the Schrodinger equation
60
Schrödinger equation for a free one dimensional particle
Solutions of the Schrodinger equation
150
2
Plane wave function
Schrödinger equation for a free one dimensional particle
68
Time-independent Schrödinger equation for a free one dimensional particle
Schrödinger equation for a free one dimensional particle
30
Particle in a box
Solutions of the Schrodinger equation
1
Quantum well
Particle in a box
Quantum harmonic oscillator
Solutions of the Schrodinger equation
168
4
Quantum LC circuit
Quantum harmonic oscillator
13
Hermite polynomials
Quantum harmonic oscillator
35
1
Hermite functions
Hermite polynomials
5
Ladder operator
Quantum harmonic oscillator
39
Quantum tunnelling
Solutions of the Schrodinger equation
22
Schrödinger equation solution for the hydrogen atom
Solutions of the Schrodinger equation
612
11
Atomic orbital
Schrödinger equation solution for the hydrogen atom
48
Quantum number
Schrödinger equation solution for the hydrogen atom
463
9
Principal quantum number
(n)
Quantum number
50
Azimuthal quantum number
(l)
Quantum number
29
4
s-orbital
Azimuthal quantum number
p-orbital
Azimuthal quantum number
d-orbital
Azimuthal quantum number
f-orbital
Azimuthal quantum number
Magnetic quantum number
(
m
l
)
Quantum number
157
Spin quantum number
(
m
s
)
Quantum number
49
1
Spectroscopic notation
Spin quantum number
49
Solutions for the Schrodinger equation with multiple particles
Solutions of the Schrodinger equation
2k
35
Separable state
(Product state)
Solutions for the Schrodinger equation with multiple particles
Solutions of the Schrodinger equation for two electrons
Solutions for the Schrodinger equation with multiple particles
134
Orbital approximation
Solutions for the Schrodinger equation with multiple particles
7
Schrödinger equation solution for the helium atom
Solutions for the Schrodinger equation with multiple particles
60
Hartree-Fock method
Solutions for the Schrodinger equation with multiple particles
732
12
Hartree-Fock method for the helium atom
Hartree-Fock method
Why do multiple electrons occupy the same orbital if electrons repel each other?
Hartree-Fock method
55
Aufbau principle
Hartree-Fock method
677
9
Electron configuration
Aufbau principle
Electron configuration notation
(
1
s
2
2
s
2
2
p
6
, 1s2 2s2 2p6)
Aufbau principle
15
Why does 2s have less energy than 1s if they have the same principal quantum number?
Aufbau principle
73
Madelung energy ordering rule
Aufbau principle
139
1
Exception to the Madelung energy ordering rule
Madelung energy ordering rule
40
Term symbol
(
2
S
1
/
2
,
2
P
1
/
2
,
2
P
3
/
2
)
Aufbau principle
423
3
Hund's rules
(1927)
Term symbol
115
2
Hund's first rule
Hund's rules
18
Hund's second rule
Hund's rules
Term symbols for carbon ground state
Solutions for the Schrodinger equation with multiple particles
731
Schrödinger equation solution for molecule
Solutions for the Schrodinger equation with multiple particles
152
16
Schrödinger equation solution for the hydrogen molecule
Schrödinger equation solution for molecule
40
Chemical bond
Schrödinger equation solution for molecule
112
14
Molecule
Chemical bond
112
6
Ball-and-stick model
Molecule
1
Isomer
Molecule
111
4
Cis-trans isomerism
Isomer
14
Enantiomer
Isomer
30
Polymorphism
(materials science)
Isomer
13
Stereochemistry
Isomer
30
Covalent bond
Chemical bond
4
Sigma bond
Covalent bond
Pi bond
Covalent bond
2
Double bond
Pi bond
Triple bond
Pi bond
Ionic bond
Chemical bond
Octet rule
Chemical bond
Two-state quantum system
Solutions of the Schrodinger equation
42
2
Bloch sphere
Two-state quantum system
22
Pauli matrix
Two-state quantum system
1
Ancestors
(8)
Schrödinger equation
Non-relativistic quantum mechanics
Quantum mechanics
Particle physics
Physics
Natural science
Science
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Incoming links
(2)
Schrödinger equation
Time-independent Schrödinger equation