Operators

Operator symbols name transformations, observables, state operators, and symmetry generators. This index records the default meanings used across the reference library and points to the canonical pages where the full definitions live.

Entries

Symbol	Default Lookup Meaning	Common Collision
$\hat H$	Hamiltonian operator and generator of time evolution.	Hilbert space $H$, magnetic field $\mathbf H$ in older notation.
$\hat x$	Position operator in one-dimensional coordinate representation.	Coordinate value $x$ or random variable $x$.
$\hat p$	Momentum operator and translation generator.	Momentum value $p$, probability $p$, pressure $p$.
$\mathbf J$	Generic or total angular momentum operator.	Current density $\mathbf j$, quantum number $j$, coupling $J$.
$\mathbf S$	Spin angular momentum operator.	Action $S$, entropy $S$, scattering matrix $S$.
$\rho$	Density operator or density matrix.	Spatial density, charge density, radial coordinate.

Reading Rule

First decide whether the symbol denotes an abstract operator, a matrix representation, a coordinate-space differential expression, or an eigenvalue. Hats are used where they prevent ambiguity, but many mature pages drop hats after declaring the convention.

References

• 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.
• B. C. Hall, Quantum Theory for Mathematicians, Springer, 2013.