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

For example, when light is incident on an interface, the standard wave equation is satisfied on both sides.

From Science Daily • Oct. 20, 2023

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

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

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

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