Derivations by Topic
Use this page when you know the subject area. Use Derivations by Method when you know the technique instead.
Formalism
Section titled “Formalism”- Schrödinger Equation
- Born Rule
- Expectation Values
- General Uncertainty Relations
- Heisenberg Equations of Motion
- Ehrenfest Theorem
Wave Mechanics and Model Systems
Section titled “Wave Mechanics and Model Systems”- Coordinate Representation
- Probability Current
- Infinite Square Well
- Harmonic Oscillator: Ladder Operators
- Harmonic Oscillator: Differential Equation
- Angular and Radial Separation
- Landau Levels
Approximation and Scattering
Section titled “Approximation and Scattering”- Nondegenerate Perturbation Theory
- Degenerate Perturbation Theory
- Fermi’s Golden Rule
- WKB Approximation
- First Born Approximation
- Partial-Wave Expansion
Composite Systems and Information
Section titled “Composite Systems and Information”Many-Body and QFT Bridge
Section titled “Many-Body and QFT Bridge”- Creation and Annihilation Operators
- One-Body Operators
- Many-Particle Hamiltonians
- Wick’s Theorem Preview
- Propagators to Path Integrals
References
Section titled “References”- R. Shankar, Principles of Quantum Mechanics, 2nd ed., Springer, 1994.
- J. J. Sakurai and J. Napolitano, Modern Quantum Mechanics, 3rd ed., Cambridge University Press, 2020.
- A. L. Fetter and J. D. Walecka, Quantum Theory of Many-Particle Systems, Dover, 2003.