In quantum mechanics, operators and observables are fundamental concepts used to describe and analyze the behavior of physical systems. While these terms are related, they have distinct meanings and roles within the theory.
Operators: In quantum mechanics, operators are mathematical entities that act on quantum states. They represent physical quantities or properties of a system and provide a way to perform mathematical operations on quantum states to obtain new states or extract information about the system. Operators are represented by matrices or differential equations and play a central role in the formalism of quantum mechanics. For example, the position operator, momentum operator, and angular momentum operator are all examples of operators in quantum mechanics.
Observables: Observables, on the other hand, are the physical quantities that can be measured or observed in an experiment. They represent the properties of a system that can be determined through measurements. Observables are associated with operators in quantum mechanics. Specifically, the values of observables correspond to the eigenvalues (possible outcomes) of the associated operators. When a measurement is performed on a quantum system, the observable collapses to one of its eigenvalues, yielding a specific measurement outcome.
To summarize, operators are mathematical objects that represent physical quantities or properties in quantum mechanics, while observables are the actual physical quantities that can be measured or observed. Operators provide a mathematical framework to describe and manipulate quantum states, while observables are the quantities that can be extracted from those states through measurements.