Steady-state concentration for particles diffusing in potential U(x) = ax²

Thread starter superwolf
Start date Apr 7, 2009
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Diffusion

2 replies · 3K views · last reply Apr 11, 2009

superwolf

Thread starter
Apr 7, 2009

N particles diffuse in one dimension in the potential U(x) = ax^2, with a > 0.
Find steady-state concentration, c0(x).

No idea how to solve this. Any equations?

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superwolf

Apr 8, 2009

Here's the answer

Typed solution text reading Ans: a. Steady state implies equilibrium, so the answer is a Boltzmann distribution; the potential is quadratic, giving a Gaussian c(x) = sqrt(a/(pi k_B T)) exp(-a x^2/(k_B T)), with dimensions 1/L for a number density in one dimension.

I still don't understand HOW they obtain that expression...

superwolf

Apr 11, 2009

Bump!

Steady-state concentration for particles diffusing in potential U(x) = ax²

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