What is the Normalization Constant for a 3D Electron Gas in Free Space?

[phrygian]

Homework Statement

In a solid state book I am reading the 3 dimensional electron gas is derived. It says, "An unconfined electron in free space is described by the Schrödinger equation where m is the free-electron mass.

The solutions of the equation, phi(r)=1/(2pi)^3 Exp(ik.r) are plane waves labelled by the wavevector k=(kx,ky,kz)."

Homework Equations

The Attempt at a Solution

I know that Exp(ikx) is not normalizble from -infinity to infinity, so how can you determine the normalization constant?

Thanks for the help

 

[icwchan]

Hint: consider identity 303 on the wikipedia page on Fourier transforms.

and this thread: https://www.physicsforums.com/showthread.php?t=166505

 

[phrygian]

But wouldn't that give 1/(2pi)^(3/2) since the x, y, and z waves each contribute 1/(2pi)^(1/2)?