Quantum states and operators are foundational concepts in quantum mechanics, providing a mathematical framework to describe and manipulate quantum systems.
Quantum States: Quantum states represent the properties of a quantum system. These states can be described by wave functions, which contain information about a particle's position, momentum, or other observable properties. Quantum states can exist in superpositions of multiple possibilities, reflecting the inherent uncertainty of quantum systems.
Quantum Operators: Quantum operators are mathematical entities that act on quantum states to represent physical observables and transformations. Operators correspond to physical quantities like position, momentum, or angular momentum. The application of an operator to a quantum state yields information about the observable's value or how the state evolves in time.
Together, quantum states and operators enable the precise description of quantum phenomena, including the behavior of particles at the quantum level, the evolution of quantum systems, and the prediction of measurement outcomes.