Number of quantum accessible states of particle given T, N?

Thread starter damarkk
Start date Wednesday, 4:16 PM
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Quantum and general physics Quantum statistical mechanics Statistical mechanics statistical-physics

Wednesday, 4:16 PM

damarkk

Homework Statement: How to find a number of accessible quantum states of a gas particle with spin S and given T, N (number of particles of the system)?

Relevant Equations: Boson gas, Fermion gas

It's given a gas of particles all identical which has T fixed and spin S. Let's ##g(\epsilon)## the density of orbital states and

##g(\epsilon) = g_0## for ##\forall \epsilon \in [\epsilon_0, \epsilon_1]##, zero otherwise.

How to compute the number of accessible quantum states of one particle?

This is my attempt, and I suspect that is not good. Let S=0 and then bosons in a system.

Simply, if we have the density of orbitals we have to integrate ##g(\epsilon)## and we have ##\int_{\epsilon_0}^{\epsilon_1} g(\epsilon) d\epsilon## and we get that is ##g_0(\epsilon_1-\epsilon_0)##.

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