Derivations by Level
Use this page to choose derivations with the right prerequisite load.
First-Course Core
Section titled “First-Course Core”- Coordinate Representation
- Born Rule
- Expectation Values
- Probability Current
- Infinite Square Well
- Harmonic Oscillator Ladder-Operator Solution
Advanced Undergraduate
Section titled “Advanced Undergraduate”- General Uncertainty Relations
- Heisenberg Equations of Motion
- Angular and Radial Separation
- Radial Schrödinger Equation
- Angular Momentum Ladder Operators
- Nondegenerate Perturbation Theory
Graduate Core
Section titled “Graduate Core”- Degenerate Perturbation Theory
- Fermi’s Golden Rule
- Lippmann-Schwinger Equation
- Partial-Wave Expansion
- Schmidt Decomposition
- Partial Trace
Research-Facing Starters
Section titled “Research-Facing Starters”- Schrieffer-Wolff Transformation
- Magnus Expansion
- Feshbach Projection Formalism
- Wick’s Theorem Preview
- Propagators to Path Integrals
- Spectral Theorem Practical
Study Rule
Section titled “Study Rule”If a derivation feels opaque, step down one level and review the prerequisite page. The goal is not to memorize a line sequence; it is to understand which assumptions move the result.
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.
- M. Reed and B. Simon, Methods of Modern Mathematical Physics, Volume I: Functional Analysis, Academic Press, 1980.