Exact solution to Fick-Jacobs equation
Juan M. Romero, O. Gonz\'alez-Gaxiola, G. Chac\'on-Acosta
TL;DR
This paper establishes a connection between the Fick-Jacobs and Schrödinger equations, providing exact solutions for the Fick-Jacobs equation with constant diffusion coefficients and analyzing the general case through variable transformation.
Contribution
It introduces a novel relation between Fick-Jacobs and Schrödinger equations and derives exact solutions for specific cases.
Findings
Exact solutions for constant diffusion coefficient case
Relation between Fick-Jacobs and Schrödinger equations
Method for analyzing the general case
Abstract
A relation between Fick-Jacobs and Schr\"{o}dinger equation is shown. When the diffusion coefficient is constant, exact solutions for Fick-Jacobs equation are obtained. Using a change of variable the general case is studied.
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Taxonomy
TopicsQuantum Mechanics and Non-Hermitian Physics · Nonlinear Photonic Systems · Quantum chaos and dynamical systems