Wave function

A complex-valued function that represents a quantum system’s state and determines probabilities for measurement outcomes. Its evolution and interpretation depend on the system and the formulation of quantum mechanics.

Schrödinger equation: A differential equation governing the time evolution of a quantum state. It specifies how a wave function changes over time when the system evolves.
Complex number: A number with real and imaginary components, commonly written using the imaginary unit. Wave-function amplitudes are generally complex, not merely real-valued.
Particle in a box: A quantum model of a particle confined within a region by idealized boundaries. Its allowed wave functions and energies illustrate quantization in a simple system.
Density matrix: An operator representing a quantum state, including statistical mixtures and subsystems. It represents states more generally than a single wave function can.
Born rule: A rule that derives measurement probabilities from a quantum state's amplitudes. Squaring a wave function’s magnitude gives position probabilities under the Born rule.
Probability density: A function whose integral over a region gives the probability of finding a quantity there. The squared magnitude of a position-space wave function defines this density.
Quantum tunneling: The passage of a quantum system through a potential barrier it could not cross classically. A wave function can extend into and beyond a classically forbidden barrier.
Pilot-wave theory: An interpretation of quantum mechanics in which particles have definite positions guided by a wave. It treats the wave function as a real guiding field alongside particle positions.
Wave function collapse: A proposed discontinuous change in a quantum state associated with measurement. It describes the state update used in some accounts of measurement.
Quantum state: A mathematical representation of the physical state of a quantum system. A wave function represents a quantum state in a particular basis.

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