English: Diagram of the dispersion relation for a particle confined in an infinitely deep well of width ${\displaystyle L}$. The dispersion curve for a free particle is shown as a grey line, which has the form

${\displaystyle E={\frac {\hbar ^{2}k^{2}}{2m}},}$

where ${\displaystyle E}$ is the energy of the particle, ${\displaystyle \hbar }$ is the reduced Planck constant, ${\displaystyle k}$ is the wavenumber of the particle and ${\displaystyle m}$ is its mass.

When the particle is confined in an infinitely deep box, only certain discrete wavenumbers and energies along this curve are permitted. The permitted points are shown as black dots along the curve and lie at wavenumbers given by

${\displaystyle k_{n}={\frac {n\pi }{L}}.}$