General solution of the three-site master equation and the discrete Riccati equation

Abstract

We first obtain by analogy with the continuous (differential) case the general solution of a discrete Riccati equation. Our results can be considered the discrete analog of Mielnik's construction in supersymmetric quantum mechanics [J. Math. Phys. 25, 3387 (1984)]. Moreover, we establish the full equivalence between our discrete Riccati equation and a corresponding homogeneous second order discrete linear equation. We present an application to the three-site master equation obtaining explicitly the general solutions for the simple cases of free random walk and the biased random walk