Wavefunction

A wavefunction is a mathematical representation of a quantum system’s state, whose squared magnitude determines probabilities for measurement outcomes. Its evolution and interpretation depend on the system and quantum theory used.

Schrödinger equation: A differential equation governing how a quantum state changes over time. It specifies the time evolution of wavefunctions in nonrelativistic quantum mechanics.
Complex number: A number with real and imaginary parts, commonly written using the imaginary unit. Wavefunctions can have complex values whose phases affect interference.
Density matrix: An operator describing a quantum state, including statistical mixtures and subsystems. It can represent states that a single wavefunction cannot describe as pure states.
Hydrogen atom: The simplest atom, consisting of one proton and one electron. Its exact wavefunctions reveal quantized energy levels and orbital shapes.
Measurement problem: The tension between continuous quantum evolution and definite measurement outcomes. It asks how wavefunction dynamics yield the single outcomes observed in experiments.
Born rule: The rule that converts a quantum state into probabilities for measurement outcomes. It assigns outcome probabilities from the wavefunction’s squared magnitude.
Hilbert space: A complete inner-product vector space used to represent quantum states. Wavefunctions are representations of state vectors in a chosen basis.
Pilot-wave theory: An interpretation of quantum mechanics in which particles have definite positions guided by a wavefunction. It treats the wavefunction as a guiding field alongside particle trajectories.
Atomic orbital: A one-electron wavefunction in an atom, associated with a particular energy state. Orbital shapes visualize spatial features of atomic wavefunctions.
Quantum decoherence: The suppression of observable interference through entanglement with an environment. It explains why wavefunction interference becomes difficult to observe, without alone selecting an outcome.

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