Consider a column of air with a base area A. Calculate the partition function and the distribution density of the particles contained in the air column taking into account the effect of the gravity on the particles.
If we consider air as an ideal gas and gravity as a constant, the Hamiltonian of the system has the following form:
N
H(qᵥ,pᵥ) = Σ (p²ᵥ / 2m ) +(1/2)mω²q²ᵥ
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