Quantum Mechanics

  1. One-Dimensional Systems
    1. Free Particle
      1. Plane Wave Solutions
        1. Momentum Eigenstates
          1. Wave Packets
            1. Group and Phase Velocity
              1. Normalization Issues
              2. Infinite Square Well
                1. Potential Definition
                  1. Boundary Conditions
                    1. Energy Quantization
                      1. Wave Functions
                        1. Parity Properties
                          1. Expectation Values
                          2. Finite Square Well
                            1. Bound States
                              1. Energy Levels
                                1. Wave Function Behavior
                                  1. Scattering States
                                    1. Transmission and Reflection
                                    2. Harmonic Oscillator
                                      1. Classical Harmonic Oscillator
                                        1. Quantum Harmonic Oscillator
                                          1. Analytical Solution
                                            1. Hermite Polynomials
                                              1. Energy Eigenvalues
                                                1. Wave Functions
                                                2. Operator Method
                                                  1. Creation and Annihilation Operators
                                                    1. Ladder Operator Algebra
                                                      1. Number States
                                                      2. Zero-Point Energy
                                                        1. Coherent States
                                                          1. Squeezed States
                                                          2. Potential Barriers and Tunneling
                                                            1. Step Potential
                                                              1. Rectangular Barrier
                                                                1. Tunneling Probability
                                                                  1. Transmission Coefficient
                                                                    1. Applications
                                                                      1. Alpha Decay
                                                                        1. Scanning Tunneling Microscopy
                                                                      2. Delta Function Potential
                                                                        1. Bound States
                                                                          1. Scattering States
                                                                            1. Resonances

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                                                                          5. Hilbert Space and Dirac Notation

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                                                                          7. Three-Dimensional Systems