What is the volime of a k-state?

[Ruizhe]

In free gas model, the vector k=π*n/L, and the volume of a k-vector is (2π)^3/V.
But I don´t understand the meaning of the volume. Why could a vector have a volume? What is the meaning of it?

 

[drvrm]

But I don´t understand the meaning of the volume. Why could a vector have a volume? What is the meaning of it?

"quantum" of the phase space,

. In 3 dimension,

actually the quantum encloses a volume element in phase space and V is the volume spanned by the wave vector

 

[BiGyElLoWhAt]

It comes from how many "k"'s you can fit in a given box, or length, or... At least I believe that's what you're referring to. From this information, you can effectively figure out the "volume" of a k-vector. It seems rather counter intuitive.
They somewhat touch on it here:
http://quantummechanics.ucsd.edu/ph130a/130_notes/node88.html
and I'll probably botch the explanation, but you can see it in action in the link above.

 

[Ruizhe]

Thanks a lot!

 

[Ruizhe]

It comes from how many "k"'s you can fit in a given box, or length, or... At least I believe that's what you're referring to. From this information, you can effectively figure out the "volume" of a k-vector. It seems rather counter intuitive.
They somewhat touch on it here:
http://quantummechanics.ucsd.edu/ph130a/130_notes/node88.html
and I'll probably botch the explanation, but you can see it in action in the link above.

Thanks