Density of states from dispersion relationship

Physics Q&A
1

Hello,

In the solution to question 1.5 of ‘Many atoms per unit cell’, dN/dk = 2L/2\pi instead of the normal L/2\pi. I did not quite understand the explanation, as you can almost always input negative values for k. I wanted to ask for further clarification, but if I had to guess it has something to do with the absolute value, as that is the main difference I see compared to the example in the lecture. In that example, we summed over all positive and negative k-values, which is why I found the solution unclear.

Thanks in advance,

Baris

2

You may regard the k as the distance to the origin. The extra factor of 2 comes from including the contributions from negative and positive k-values. Try to write down an expression for the nr of states between 2 energies, and you will see the factor 2 appear.