What is the Relation Between k and x in the Given Energy Function?

[dikmikkel]

Homework Statement

I have an energy function as follows:
E = \dfrac{\hbar^2}{2m_e}k_x^2+E_0\left(n_y^2+1\right)
Where E_0 = \dfrac{\pi^2\hbar^2}{2m_eL_z}
I am asked to plot this energy for x\in ]-L_z/2;L_z/2[
I know everything but not the relation between k and x?.

The Attempt at a Solution

I Fourier transform the energy from x to k-space(momentum space) and get some dela functions in k multiplied on as one would expect, but this seems odd to me and I want to know:
What is the relation between k and x?

 

[dikmikkel]

Follow up:
Maybe I shall choose some k and just plot a constant, but it seems silly.