Derivations by Method
Use this page when the technique matters more than the physical topic.
Operator Algebra
Section titled “Operator Algebra”- Heisenberg Equations of Motion
- Ehrenfest Theorem
- General Uncertainty Relations
- Harmonic Oscillator Ladder-Operator Solution
- Angular Momentum Ladder Operators
Differential Equations and Boundary Conditions
Section titled “Differential Equations and Boundary Conditions”- Time-Independent Schrödinger Equation
- Infinite Square Well
- Harmonic Oscillator Differential-Equation Solution
- Radial Schrödinger Equation
- Boundary Conditions
Symmetry and Representations
Section titled “Symmetry and Representations”- Angular Momentum Algebra
- Spherical Harmonics
- Clebsch–Gordan Coefficients
- Wigner Symbols
- Commutators and Conservation Laws
Perturbative and Variational Methods
Section titled “Perturbative and Variational Methods”- Nondegenerate Perturbation Theory
- Degenerate Perturbation Theory
- Variational Principle
- Fermi’s Golden Rule
- Schrieffer-Wolff Transformation
Green Functions and Scattering
Section titled “Green Functions and Scattering”- Lippmann-Schwinger Equation
- First Born Approximation
- Partial-Wave Expansion
- Optical Theorem
- Free-Particle Propagator
Density Operators and Channels
Section titled “Density Operators and Channels”References
Section titled “References”- C. Cohen-Tannoudji, B. Diu, and F. Laloe, Quantum Mechanics, Wiley, 1977.
- J. J. Sakurai and J. Napolitano, Modern Quantum Mechanics, 3rd ed., Cambridge University Press, 2020.
- M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, 2010.