Operators | Operators in Classical and Quantum Mechanics | Properties of Operators

In quantum mechanics, operators are mathematical entities that represent observables or physical quantities. 

Operatirs describe how mathematical functions (wavefunctions) transform under specific physical operations or measurements. 

These operators operate on wavefunctions to produce new wavefunctions or eigenfunctions, and they can be used to calculate expectation values of observable quantities.

The most common operator in quantum mechanics is the Hamiltonian operator (H), which represents the total energy of a system. Other commonly used operators include the position operator (x), momentum operator (p), angular momentum operator (L), and spin operator (S). Each of these operators has specific properties and mathematical properties.

Operators in quantum mechanics can be represented as matrices, called operator matrices or matrix representations, but they can also be represented using differential or integral expressions.