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Physics
Quantum Physics
Quantum Mechanics
1. Historical Development and Foundations
2. Mathematical Foundations
3. Wave Function Formalism
4. Quantum Mechanical Operators
5. Hilbert Space and Dirac Notation
6. One-Dimensional Systems
7. Three-Dimensional Systems
8. Angular Momentum Theory
9. The Hydrogen Atom
10. Approximation Methods
11. Identical Particles and Many-Body Systems
12. Scattering Theory
13. Quantum Mechanics of Radiation
14. Relativistic Quantum Mechanics
15. Interpretations and Foundations
16. Advanced Topics
3.
Wave Function Formalism
3.1.
The Quantum State
3.1.1.
Wave Function Definition
3.1.2.
Physical Interpretation
3.1.3.
Probability Amplitude
3.1.4.
Complex Nature
3.1.5.
Normalization
3.1.5.1.
Normalization Condition
3.1.5.2.
Physical Meaning
3.1.5.3.
Finite and Infinite Domains
3.1.6.
Boundary Conditions
3.1.6.1.
Continuity Requirements
3.1.6.2.
Differentiability
3.1.6.3.
Asymptotic Behavior
3.2.
Probability and Measurement
3.2.1.
Born Rule
3.2.2.
Probability Density
3.2.3.
Probability Current
3.2.4.
Conservation of Probability
3.2.5.
Measurement Postulates
3.3.
Time Evolution
3.3.1.
Time-Dependent Schrödinger Equation
3.3.1.1.
Mathematical Form
3.3.1.2.
Physical Interpretation
3.3.1.3.
Hamiltonian Operator
3.3.2.
Time-Independent Schrödinger Equation
3.3.2.1.
Stationary States
3.3.2.2.
Energy Eigenvalue Problem
3.3.2.3.
Separation of Variables
3.3.3.
General Solution Structure
3.3.3.1.
Superposition of Stationary States
3.3.3.2.
Time Evolution of Coefficients
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4. Quantum Mechanical Operators