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

[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 $g_0(\epsilon_1-\epsilon_0)$.

 

[WWGD]

It seems that we have N particles with spin S in contact with a heat bath at temperature T. OK.
That is enough to specify the number of accessible states as (2S+1). Setting the spin equal to zero would result in one state only.
In the absence of a perturbation, e.g. an external magnetic field, the (2S+1) states are degenerate which makes them equally accessible at any temperature.
Also, I do not understand the bit about orbital states. Whence orbital states? Presumably the particles are free.

Can you give us the original statement /question as you were given, damarkk?

Attn @kuruman