Core Formalism Derivations
Core formalism derivations explain why the compact postulates produce the standard calculational rules. They are the right starting point when a later page uses a formula without rederiving it.
Probability and Expectation
Section titled “Probability and Expectation”- Born Rule
- Born Rule: Discrete
- Born Rule: Continuous
- Expectation Values
- Variance and Standard Deviation
Operators and Compatibility
Section titled “Operators and Compatibility”- Commutators
- Canonical Commutation Relations
- General Uncertainty Relations
- Position-Momentum Uncertainty
- Spectral Decomposition
Dynamics
Section titled “Dynamics”- Schrödinger Equation
- Energy Eigenstates
- Conservation Laws
- Heisenberg Equations of Motion
- Ehrenfest Theorem
- Interaction Picture
Density Operators
Section titled “Density Operators”References
Section titled “References”- J. von Neumann, Mathematical Foundations of Quantum Mechanics, Princeton University Press, 1955.
- R. Shankar, Principles of Quantum Mechanics, 2nd ed., Springer, 1994.
- B. C. Hall, Quantum Theory for Mathematicians, Springer, 2013.