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Non-relativistic quantum mechanics

| nosplit | ↑ parent "Quantum mechanics" | words: 26 | descendant words: 5k | descendants: 66

nosplit | ⇓ toc | ↑ parent "Quantum mechanics" | words: 26 | descendant words: 5k | descendants: 66

The first quantum mechanics theories developed.

Their most popular formulation has been the Schrödinger equation.

Table of contents | 26, 5k, 66
- Schrödinger equation | 555, 5k, 60 | 🔗 link | nosplit | ↑ parent "Non-relativistic quantum mechanics"
  - Time-independent Schrodinger equation | 416 | 🔗 link | nosplit | ↑ parent "Schrödinger equation"
  - Derivation of the Schrodinger equation | 99, 152, 1 | 🔗 link | nosplit | ↑ parent "Schrödinger equation"
    - Why are complex numbers used in the Schrodinger equation? | 53 | 🔗 link | nosplit | ↑ parent "Derivation of the Schrodinger equation"
  - Solutions of the Schrodinger equation | 34, 2k, 35 | 🔗 link | nosplit | ↑ parent "Schrödinger equation"
    - Schrodinger equation simulations | 279, 348, 1 | 🔗 link | nosplit | ↑ parent "Solutions of the Schrodinger equation"
      - Why it is hard to simulate quantum systems? | 69 | 🔗 link | nosplit | ↑ parent "Schrodinger equation simulations"
    - Schrodinger equation for a one dimensional particle | 135 | 🔗 link | nosplit | ↑ parent "Solutions of the Schrodinger equation"
    - Schrodinger equation for a free one dimensional particle | 12, 12, 1 | 🔗 link | nosplit | ↑ parent "Solutions of the Schrodinger equation"
      - Time independent Schrodinger equation for a free one dimensional particle | 🔗 link | nosplit | ↑ parent "Schrodinger equation for a free one dimensional particle"
    - Particle in a box | 🔗 link | nosplit | ↑ parent "Solutions of the Schrodinger equation"
    - Quantum harmonic oscillator | 130, 235, 3 | 🔗 link | nosplit | ↑ parent "Solutions of the Schrodinger equation"
      - Hermite polynomials | 43, 55, 1 | 🔗 link | nosplit | ↑ parent "Quantum harmonic oscillator"
        
        Hermite functions | 12 | 🔗 link | nosplit | ↑ parent "Hermite polynomials"
      - Ladder operator | 50 | 🔗 link | nosplit | ↑ parent "Quantum harmonic oscillator"
    - Quantum tunnelling | 36 | 🔗 link | nosplit | ↑ parent "Solutions of the Schrodinger equation"
    - Schrodinger equation solution for the hydrogen atom | 159, 374, 4 | 🔗 link | nosplit | ↑ parent "Solutions of the Schrodinger equation"
      - Atomic orbital | 80, 215, 3 | 🔗 link | nosplit | ↑ parent "Schrodinger equation solution for the hydrogen atom"
        
        Principal quantum number (n) | 71 | 🔗 link | nosplit | ↑ parent "Atomic orbital"
        
        Azimuthal quantum number (l) | 12 | 🔗 link | nosplit | ↑ parent "Atomic orbital"
        
        Magnetic quantum number (m_l) | 52 | 🔗 link | nosplit | ↑ parent "Atomic orbital"
    - Solutions for the Schrodinger equation with multiple particles | 20, 680, 15 | 🔗 link | nosplit | ↑ parent "Solutions of the Schrodinger equation"
    - Two-state quantum system | 60, 108, 2 | 🔗 link | nosplit | ↑ parent "Solutions of the Schrodinger equation"
      - Bloch sphere | 40 | 🔗 link | nosplit | ↑ parent "Two-state quantum system"
      - Pauli matrix | 8 | 🔗 link | nosplit | ↑ parent "Two-state quantum system"
  - Born-Oppenheimer approximation | 🔗 link | nosplit | ↑ parent "Schrödinger equation"
  - Uncertainty principle | 509, 1k, 10 | 🔗 link | nosplit | ↑ parent "Schrödinger equation"
    - Position and momentum space | 187, 435, 4 | 🔗 link | nosplit | ↑ parent "Uncertainty principle"
      - Position representation | 95 | 🔗 link | nosplit | ↑ parent "Position and momentum space"
      - Position operator | 38 | 🔗 link | nosplit | ↑ parent "Position and momentum space"
      - Momentum operator | 115 | 🔗 link | nosplit | ↑ parent "Position and momentum space"
      - Squeezed coherent state | 🔗 link | nosplit | ↑ parent "Position and momentum space"
    - Energy operator | 24, 52, 1 | 🔗 link | nosplit | ↑ parent "Uncertainty principle"
      - Time-energy uncertainty principle | 28 | 🔗 link | nosplit | ↑ parent "Energy operator"
    - Angular momentum operator | 217, 226, 1 | 🔗 link | nosplit | ↑ parent "Uncertainty principle"
      - Total angular momentum operator | 9 | 🔗 link | nosplit | ↑ parent "Angular momentum operator"
    - Complementarity (physics) | 🔗 link | nosplit | ↑ parent "Uncertainty principle"
  - Conservation laws in Schrodinger equations | 20, 86, 2 | 🔗 link | nosplit | ↑ parent "Schrödinger equation"
    - Conservation of the square amplitude in the Schrodinger equation | 66, 66, 1 | 🔗 link | nosplit | ↑ parent "Conservation laws in Schrodinger equations"
      - Probability current | 🔗 link | nosplit | ↑ parent "Conservation of the square amplitude in the Schrodinger equation"
  - Wave function ( $ψ$ ) | 107, 195, 5 | 🔗 link | nosplit | ↑ parent "Schrödinger equation"
    - Matter wave (1923) | 0, 88, 4 | 🔗 link | nosplit | ↑ parent "Wave function"
      - Electron diffraction experiment | 0, 4, 2 | 🔗 link | nosplit | ↑ parent "Matter wave"
        
        Diffraction of Cathode Rays by a Thin Film by Thomson and Reid (1927) | 4 | 🔗 link | nosplit | ↑ parent "Electron diffraction experiment"
        
        Davisson-Germer experiment (1927) | 🔗 link | nosplit | ↑ parent "Electron diffraction experiment"
      - de Broglie relations | 84 | 🔗 link | nosplit | ↑ parent "Matter wave"
- Equivalent alternatives to the Schrodinger equation | 6, 309, 4 | 🔗 link | nosplit | ↑ parent "Non-relativistic quantum mechanics"
  - Matrix mechanics (1925) | 225, 292, 2 | 🔗 link | nosplit | ↑ parent "Equivalent alternatives to the Schrodinger equation"
    - Quantum mechanical re-interpretation of kinematic and mechanical relations by Heisenberg (1925) (Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen) | 67 | 🔗 link | nosplit | ↑ parent "Matrix mechanics"
    - Heisenberg picture | 🔗 link | nosplit | ↑ parent "Matrix mechanics"
  - De Broglie-Bohm theory | 11 | 🔗 link | nosplit | ↑ parent "Equivalent alternatives to the Schrodinger equation"

Ancestors

Quantum mechanics | 169, 20k, 270
Particle physics | 137, 32k, 511
Physics | 276, 47k, 835
Natural science | 0, 64k, 2k
Science | 0, 69k, 2k
Ciro Santilli's Homepage | 262, 237k, 4k

Incoming links

Path integral formulation | 138, 204, 3
Quantum field theory | 329, 8k, 109
Lecture 1 | 257
Quantum mechanics | 169, 20k, 270
Shelter Island Conference | 156, 243, 1