Dear all,
What if the density of something seams to be negative?
If I am well, the density of states, electrons or holes should always be positive. But what if the expression of some density has (sometimes) a negative sign? For example because it depends on a sine-function?
1. Should in such a case \sin(E) be |\sin(E)|?
If this is true, I have a follow-up question:
2. Why cannot we say in general that g(E) = \frac{dN}{dk} |\frac{dk}{dE}| instead of g(E) = \frac{dN}{dk} \frac{dk}{dE} ?
In the last working class I learned that this is not allowed.
example where this is not allowed
In question 6.2 of the extra excercises, g_{vb}(E) \alpha \frac{-1}{t_{vb}} because \frac{dk}{dE}= \frac{-1}{t_{vb}} . Here it is not allowed to say that g_{vb} \alpha |\frac{-1}{t_{vb}}|. The conclusion should be that t_{vb} is negative.