Atomic and Molecular Physics

  1. The Hydrogen Atom
    1. The Central Potential Problem
      1. Coulomb Potential Energy
        1. Two-Body Problem Reduction
          1. Center-of-Mass Transformation
            1. Reduced Mass
              1. Separation of Variables in Spherical Coordinates
                1. Radial Equation
                  1. Angular Equation
                  2. Solution of the Hydrogen Atom
                    1. The Radial Schrödinger Equation
                      1. Effective Potential
                        1. Centrifugal Barrier Term
                          1. Asymptotic Behavior
                            1. Series Solution Method
                              1. Associated Laguerre Polynomials
                                1. Normalization of Radial Functions
                                2. Quantum Numbers and Energy Levels
                                  1. Principal Quantum Number n
                                    1. Physical Meaning and Allowed Values
                                      1. Orbital Angular Momentum Quantum Number l
                                        1. Physical Meaning and Allowed Values
                                          1. Magnetic Quantum Number m_l
                                            1. Physical Meaning and Allowed Values
                                              1. Energy Level Formula
                                                1. Degeneracy of Energy Levels
                                                  1. Accidental Degeneracy in Hydrogen
                                                  2. Hydrogen Atom Wavefunctions
                                                    1. Complete Wavefunctions
                                                      1. Radial Wavefunctions
                                                        1. Radial Nodes
                                                          1. Radial Probability Distribution
                                                            1. Angular Wavefunctions
                                                              1. Spherical Harmonics
                                                                1. Atomic Orbitals
                                                                  1. s Orbitals (l = 0)
                                                                    1. p Orbitals (l = 1)
                                                                      1. d Orbitals (l = 2)
                                                                        1. f Orbitals (l = 3)
                                                                          1. Orbital Shapes and Orientations
                                                                            1. Probability Density Plots
                                                                              1. Nodal Surfaces
                                                                                1. Radial and Angular Nodes

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                                                                              2. Simple Quantum Systems

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                                                                              4. Fine Structure and Relativistic Effects