Abstract
The Fokker–Planck equation with a constant diffusion coefficient and a particular polynomial drift coefficient can exhibit a bistable equilibrium distribution. Such model systems have been used to study chemical reactions, nucleation, climate, optical bistability and other phenomena. In this paper, we consider a particular choice for the drift coefficient of the form $$A(x) = x^5 - x^3$$ to exemplify the statistical behaviour of such systems. The transformation of the Fokker–Planck equation to a Schrodinger equation leads to a potential that belongs to the class of potentials in supersymmetric (SUSY) quantum mechanics. A pseudospectral method based on nonclassical polynomials is used to determine the spectrum of the Fokker–Planck operator and of the Schrodinger equation. The converged numerical eigenvalues are compared with WKB and SWKB approximations of the eigenvalues.
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