Wave function

Definition

A wave function is a mathematical representation that describes the amplitude of a wave at each point in space and time. It encapsulates the properties of waves such as frequency, wavelength, and phase.

5 Must Know Facts For Your Next Test

1. The wave function is often denoted by $\psi(x,t)$, where $x$ represents position and $t$ represents time.
2. Wave functions can describe both standing waves and traveling waves.
3. $\psi(x,t)$ typically takes on complex values, but physical interpretations often consider its magnitude or real part.
4. The square of the amplitude of a wave function corresponds to the intensity or probability density of the wave.
5. Superposition principle states that if $\psi_1$ and $\psi_2$ are solutions, then any linear combination $a\psi_1 + b\psi_2$ is also a solution.

Review Questions

• What does the wave function $\psi(x,t)$ represent in terms of physical properties?
• How does the superposition principle apply to wave functions?
• What is the relationship between the square of the amplitude of a wave function and intensity?

Related terms

Amplitude:

The maximum displacement or distance moved by a point on a vibrating body or wave measured from its equilibrium position.

Frequency:

The number of oscillations (cycles) that occur in one second, measured in Hertz (Hz).

Wavelength:

The distance between successive crests, troughs, or identical points in adjacent cycles of a waveform signal propagated in space or along a wire.