Factorization of the Non‐stationary Heat Equation

Abstract

In this paper we describe a factorization of the heat operator ∆x − ∂t based on methods of Clifford analysis, in order to reduce the non-stationary Schroedinger equation to a first order differential equation, which is the direct n-dimensional generalization of the ordinary differential Riccati equations.

On a factorization of the Schrödinger and Klein–Gordon operators

“…In [8][9][10][11] the authors proposed a scheme to factorize time-dependent operators, in particular, parabolic operators by means of joining elements of the Witt basis. This was extended to the time-dependent Schrödinger equation [12][13][14].…”