Wave mechanics

A formulation of quantum mechanics that represents physical states with wavefunctions and describes their evolution using the Schrödinger equation.

Schrödinger equation: A differential equation governing how a quantum state changes over time. It supplies the central dynamical law for wavefunctions.
Louis de Broglie: A French physicist who proposed that matter has wave-like properties associated with its momentum. His matter-wave hypothesis supplied a key premise for wave mechanics.
Hilbert space: A complete inner-product vector space used to represent states in quantum mechanics. Wavefunctions are one representation of vectors in this abstract state space.
Matrix mechanics: A formulation of quantum mechanics that represents observables and transitions using matrices and algebraic arrays. It reached the same physical predictions through a formulation distinct from wavefunctions.
Particle in a box: An idealized quantum system in which a particle is confined by infinitely high potential walls. Its boundary conditions produce discrete energies and standing-wave states.
Wavefunction: A mathematical representation of a quantum state, whose amplitudes determine measurement probabilities. Wave mechanics expresses physical states through this object.
Erwin Schrödinger: An Austrian physicist who developed the wave equation central to wave mechanics. He formulated the theory’s defining equation in 1926.
Complex number: A number with real and imaginary components, often written using the unit imaginary number i. Quantum wavefunctions generally take complex values.
Heisenberg picture: A quantum-mechanical representation in which operators evolve over time while the state is fixed. It shifts time dependence from states to operators, unlike the Schrödinger picture.
Quantum harmonic oscillator: A quantum system whose potential energy varies quadratically with displacement from equilibrium. Its exact wavefunctions and evenly spaced energy levels make it a foundational model.

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