Physics – Mathematical Physics
Scientific paper
2011-08-03
Physics
Mathematical Physics
16 pages, no figures
Scientific paper
It is shown a relation between the Fick-Jacobs equation and Schr\"{o}dinger equation. The Fick-Jacobs equation describes the diffusion in a channel with a shape of a surface of revolution. For the case of constant diffusion coefficient the following results are obtained: the case of the conical channel is mapped to quantum free particle; if the shape of channel is a throat is obtained a relation with quantum particle in a constant potential; also the sinusoidal channel is related with quantum particle in a constant potential; in addition, when the channel cross section varies as a quadratic exponential, is shown its equivalence with the quantum harmonic oscillator. The general case of variable diffusion coefficient is also considered. In this case a change of variable is proposed, and if it is invertible, the Fick-Jacobs equation is equivalent to the Schr\"{o}dinger equation of a particle in an effective potential.
Chacon-Acosta Guillermo
Gonzalez-Gaxiola O.
Romero Juan M.
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