wave equation

American  

noun

1. Mathematics, Physics. any differential equation that describes the propagation of waves or other disturbances in a medium.

2. Physics. any of the fundamental equations of quantum mechanics whose solutions are possible wave functions of a particle.

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wave equation British  

noun

1. physics a partial differential equation describing wave motion. It has the form ∇²φ = (1/ c ²) × (∂²φ/∂ t ²), where ∇² is the Laplace operator, t the time, c the speed of propagation, and φ is a function characterizing the displacement of the wave

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wave equation Scientific  

1. A partial differential equation that describes the shape and movement of waves, given a set of boundary conditions (such as the initial shape of the wave, or the evolution of a force affecting the wave).

2. The fundamental equation of wave mechanics.

3. See also Schrödinger's equation

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Etymology

Origin of wave equation

First recorded in 1925–30

Example Sentences

A standard wave equation describes how a "wave function" changes over time and across space.

From Science Daily • Mar. 10, 2026

Quantum theory describes fundamental particles not just as physical waves but also as being determined by the so-called wave equation, whose solutions may be designated by the Greek letter psi, ψ.

From Scientific American • Jan. 8, 2020

Thus, it appears that while electrons are small localized particles, their motion does not follow the equations of motion implied by classical mechanics, but instead it is governed by some type of a wave equation.

From Textbooks • Feb. 14, 2019

As befits the concept of complementarity, there are two completely different but ultimately equivalent mathematical formulations of quantum phenomena — Erwin Schrodinger’s wave equation and Werner Heisenberg’s matrix mechanics, the latter highlighting particle-like behavior.

From Washington Post • Mar. 30, 2018

Erwin Schrödinger, whose wave equation, in spite of his misgivings, became the foundation of the standard indeterminate view of quantum physics.

From Forbes • Mar. 13, 2014