# Dispersion relation (particle in a box)

I am learning some basic solid state physics idea, like density of state ...etc.

For particle in a 1D box,

E = n^2 (pi)^2 (h_bar)^2 / 2mL^2

But why it is written as
E = (h_bar)^2 k^2 /2m

does it means that energy eigenvalue E is related to momentum k ?
I guess it is not because momentum is not eigenstate.

But what is this expression talking about anyway ? what is the physical meaning of this k ?