- #1
AndersF
- 27
- 4
- TL;DR Summary
- Reexpress the density of states for a Fermion gas in terms of momentum in terms of the energy.
I have a problem where I am given the density of states for a Fermion gas in terms of momentum: ##D(p)dp##. I need to express it in terms of the energy of the energy levels, ##D(\varepsilon)d\varepsilon##, knowing that the gas is relativistic and thus ##\varepsilon=cp##.
Replacing ##p## by ##\varepsilon/c## and ##dp## by ##d\varepsilon/c##, I would get ##D(\varepsilon/c)d\varepsilon/c##, but I'm looking for ##D(\varepsilon)d\varepsilon## instead.
I'm missing something? I know this is basic stuff, but I am stuck and this issue has me clueless...
Replacing ##p## by ##\varepsilon/c## and ##dp## by ##d\varepsilon/c##, I would get ##D(\varepsilon/c)d\varepsilon/c##, but I'm looking for ##D(\varepsilon)d\varepsilon## instead.
I'm missing something? I know this is basic stuff, but I am stuck and this issue has me clueless...