Concept Glossary

This concept glossary is a lookup layer for recurring quantum mechanics terms. It gives compact definitions, points to each concept’s canonical teaching page, and records common confusions that often cause mistakes in calculations or interpretation.

Use it when you need a fast reminder. Use the linked canonical homes when you need derivations, examples, assumptions, or edge cases.

Core Entries

Entry	Compact Role	Canonical Route
Amplitude	Complex number whose squared modulus contributes to a probability.	Probability Amplitudes
Born Rule	Rule assigning measurement probabilities from amplitudes, projectors, or density operators.	Born Rule
Commutator	Operator difference measuring order-dependence and noncommutativity.	Commutators
Decoherence	Suppression of locally observable interference through entanglement with uncontrolled degrees of freedom.	Decoherence Preview
Density Matrix	Matrix representation of a density operator for pure or mixed states.	Density Operators
Eigenstate	State associated with a sharp eigenvalue of an operator.	Eigenvalues and Eigenstates
Entanglement	Non-factorization across a specified subsystem split.	Entangled States
Hamiltonian	Generator of time evolution and, in standard settings, the energy observable.	Hamiltonians
Hilbert Space	Complete inner-product space used for states and amplitudes.	Hilbert Spaces
Observable	Measurable quantity represented by a self-adjoint operator.	Observables
Superposition	Linear combination whose physical content depends on amplitudes, basis, and relative phase.	Superposition and Relative Phase
Wavefunction	Coordinate-space amplitude representation of a state.	Coordinate Representation

Entry Anatomy

Each entry is deliberately compact. A mature entry should give:

• a one-paragraph definition;
• a formula hook or symbol convention when useful;
• a canonical home for the full treatment;
• common confusions and aliases;
• links to nearby glossary entries;
• references to standard sources.

When to Use Canonical Pages

The glossary should not duplicate derivations. For example, the commutator entry can state $[A,B]=AB-BA$, but the canonical page explains compatibility, uncertainty relations, and dynamics. The amplitude entry can record $P=\lvert\alpha\rvert^2$, but the Born-rule pages explain measurement contexts and degeneracy.

Common Glossary Mistakes

• Treating a compact definition as a complete set of hypotheses.
• Reading formulas without checking normalization, domains, spectra, or basis conventions.
• Confusing a representation-dependent object, such as a matrix or wavefunction, with the underlying abstract state or operator.
• Using a glossary entry to settle an interpretive question that belongs on a longer foundations or measurement page.

References

• L. E. Ballentine, Quantum Mechanics: A Modern Development, 2nd ed., World Scientific, 2014.
• D. J. Griffiths and D. F. Schroeter, Introduction to Quantum Mechanics, 3rd ed., Cambridge University Press, 2018.
• J. J. Sakurai and J. Napolitano, Modern Quantum Mechanics, 3rd ed., Cambridge University Press, 2020.
• R. Shankar, Principles of Quantum Mechanics, 2nd ed., Springer, 1994.