when I'm going through the online Density of States(DOS) deriving courses, I find that there seem to be 2 set of boundary condition which will lead to the same result.
Note: K is the one in p=(h/2π)K L is the length of the material
Conditon 1： Thinking of the material as a 1D/2D/3D potential well. And electron moving inside is considered as stand wave. So K=π/L*N N= 1,2,3,4,5.... Because it's stand wave, so the k=1 and k=-1 is the same wave.
Condition 2: Considering the material as a 1D/2D/3D potential well. And electron moving inside is under Bon-Von Karman condition. So K=2π/L*N, N=±1,±2,±3,±4...... Because when the electron reach one end of the material it is considered to instantly moved the begin place. So K=1 is not the same as k=-1
which one is more reasonable?