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Introduction to Quantum Mechanics

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2018/10/30 Share

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Author:2LalA猪

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Published on:30th October 2018, 9:01 pm

Updated on:9th June 2020, 3:19 pm

License:CC BY 4.0

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    CATALOG
    1. 1. Fundamentals
      1. 1.1. Postulates of QM
      2. 1.2. Operators
        1. 1.2.1. Common Operators
        2. 1.2.2. Derivation of Operators
        3. 1.2.3. Eigenvalues and Eigenfunctions
        4. 1.2.4. Commutators
        5. 1.2.5. Notations
        6. 1.2.6. Hermitian Operators
      3. 1.3. Uncertainty
        1. 1.3.1. Heisenberg uncertainty principle
    2. 2. Wavefunctions
      1. 2.1. Schroedinger Equations
      2. 2.2. Characteristics of Wavefunctions
      3. 2.3. 1-D Free Particles
      4. 2.4. An infinitely thick potential wall
      5. 2.5. A barrier of finite width
      6. 2.6. Particle in a box
      7. 2.7. Harmonic Oscillator
        1. 2.7.1. Ground state and ZPE
        2. 2.7.2. Scaled Coordinate
        3. 2.7.3. Higher order solutions
        4. 2.7.4. Properties of solutions
      8. 2.8. Morse Oscillator
    3. 3. Angular Momentum
      1. 3.1. Operators
      2. 3.2. Commutators
      3. 3.3. Spherical polar coordinates
      4. 3.4. Eigenfunctions
        1. 3.4.1. J_z
        2. 3.4.2. J^2
      5. 3.5. Shift Operators
      6. 3.6. Rigid rotor
      7. 3.7. Rotation-Vibration
    4. 4. Getting Real
      1. 4.1. Born-Oppenheimer approximation
      2. 4.2. Hydrogen atom
        1. 4.2.1. Atomic units
        2. 4.2.2. Wavefunctions
        3. 4.2.3. Radial probability density
      3. 4.3. Many-electron atoms
        1. 4.3.1. Helium
        2. 4.3.2. Central field approximation
        3. 4.3.3. Self-Consistent Field method
      4. 4.4. Orbital energies
    5. 5. Spin
      1. 5.1. Electron spin
      2. 5.2. Overall wavefunctions
      3. 5.3. Spins of two electrons
      4. 5.4. Pauli Principle
        1. 5.4.1. Antisymmetric functions
        2. 5.4.2. Fermi Holes
        3. 5.4.3. Coulombic and Exchange integrals
        4. 5.4.4. Multi-electron atom obeying Pauli
        5. 5.4.5. Electron correlation
      5. 5.5. Hund’s Rule
        1. 5.5.1. Terminology
        2. 5.5.2. Rules
        3. 5.5.3. Explaining ionisation energy trend
      6. 5.6. Spin-orbit coupling
    6. 6. Approximation Methods
      1. 6.1. Variation Method
        1. 6.1.1. Variation principle
        2. 6.1.2. For wavefunctions with one parameter
        3. 6.1.3. For multiple parameters