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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
4.
Quantum Mechanical Operators
4.1.
Operator Formalism
4.1.1.
Linear Operators
4.1.2.
Operator Algebra
4.1.3.
Commutators
4.1.3.1.
Definition and Properties
4.1.3.2.
Commutator Relations
4.1.3.3.
Uncertainty Relations
4.2.
Observable Operators
4.2.1.
Hermitian Operators
4.2.2.
Eigenvalue Equations
4.2.3.
Spectral Decomposition
4.2.4.
Measurement Theory
4.3.
Fundamental Operators
4.3.1.
Position Operator
4.3.2.
Momentum Operator
4.3.3.
Hamiltonian Operator
4.3.4.
Angular Momentum Operators
4.4.
Expectation Values
4.4.1.
Definition and Calculation
4.4.2.
Time Dependence
4.4.3.
Ehrenfest's Theorem
4.5.
Uncertainty Principle
4.5.1.
Heisenberg Uncertainty Relations
4.5.2.
Position-Momentum Uncertainty
4.5.3.
Energy-Time Uncertainty
4.5.4.
Generalized Uncertainty Relations
4.5.5.
Physical Interpretation
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3. Wave Function Formalism
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5. Hilbert Space and Dirac Notation