Quantum Mechanics

  1. Wave Function Formalism
    1. The Quantum State
      1. Wave Function Definition
        1. Physical Interpretation
          1. Probability Amplitude
            1. Complex Nature
              1. Normalization
                1. Normalization Condition
                  1. Physical Meaning
                    1. Finite and Infinite Domains
                    2. Boundary Conditions
                      1. Continuity Requirements
                        1. Differentiability
                          1. Asymptotic Behavior
                        2. Probability and Measurement
                          1. Born Rule
                            1. Probability Density
                              1. Probability Current
                                1. Conservation of Probability
                                  1. Measurement Postulates
                                  2. Time Evolution
                                    1. Time-Dependent Schrödinger Equation
                                      1. Mathematical Form
                                        1. Physical Interpretation
                                          1. Hamiltonian Operator
                                          2. Time-Independent Schrödinger Equation
                                            1. Stationary States
                                              1. Energy Eigenvalue Problem
                                                1. Separation of Variables
                                                2. General Solution Structure
                                                  1. Superposition of Stationary States
                                                    1. Time Evolution of Coefficients

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                                                2. Mathematical Foundations

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                                                4. Quantum Mechanical Operators