What Specifies Energy Bands in Solid?

[mkbh_10]

n is the band index and k is the electron wave vector. Now is energy band specified when for each n , k runs through all the values available that specify periodic boundary conditions ?

But in Ashcroft Mermin , it is also given that for a given k , there exists an infinite family of solutions labelled by n which is the band index.

I am confused here about what specifies the band.

 

[DrDu]

Look at it like this: k determines the boundary conditions for an elementary cell, namely the value of the logarithmic derivative of the wavefunktion $\psi'/\psi (a)=\psi'/\psi(0) \exp(ika)$.
Now the Schroedinger equation in a single cell, with the boundary condition specified by k, has an infinity of solutions labelled by n.

 

[mkbh_10]

So the second one is correct ans.