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.

---

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

---

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

---

Etymology

Origin of wave equation

First recorded in 1925–30

Example Sentences

See Examples For:

wave equation

Schrödinger's wave equation also made it possible to correctly analyze the hydrogen atom, which contains just one electron.

From Science Daily ● Mar. 10, 2026

We found that the interference pattern we measured did not match the approximate solution to the wave equation given by ψA + ψB, but it did match the solution that included the nonzero Sorkin parameter.

From Scientific American ● Jan. 8, 2020

This “many worlds interpretation” of the wave equation is an extravagant — some say desperate — attempt to make sense of quantum waving-ness.

From Washington Post ● Aug. 9, 2018

Substituting into our wave equation, we get c = λ × f.

From Textbooks ● Oct. 13, 2016

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