# Formula Dispersion Relation for a Crystal with a Monatomic Basis Angular frequency    Angular wavenumber    Spring constant    Mass    Lattice constant

## Angular frequency

Unit
This dispersion relation $$\omega(k)$$ describes the relation between the frequency (energy) and the wavenumber (wavelength) of a monatomic chain of a crystal. The oscillation is purely longitudinal (or transversal) and only the interaction between the neighboring chains is considered here.

The angular frequency is related to the frequency $$f$$ via $$\omega = 2\pi \, f$$.

## Angular wavenumber

Unit
Wavenumber is related to wavelength $$\lambda$$ via $$k = 2\pi / \lambda$$.

## Spring constant

Unit
Spring constant (or coupling constant) comes from the Hooke's law and describes how much an atomic chain is coupled to its neighboring chains.

## Mass

Unit
Mass of an atom within the chain.

## Lattice constant

Unit
Lattice constant is the distance between two chains when they are in equilibrium (i.e. not deflected).