What Defines a Solenoidal Vector Field?

tweedle2
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Homework Statement
So I know how to work out if a vector field is incompressible normally, the divergence is 0. However I don't know how to do it for cylindrical or spherical coordinates, can anyone help me
Relevant Equations
Div f = 0
ac.PNG
 
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Thread 'Number of quantum accessible states of a particle given T, N?'

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...
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