Nonlinear Phenomena in Complex Systems, 2026, Vol.29, No.2, pp.113

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2026, Vol.29, No.2, pp.113 - 136

Pauli Equation in 12 Systems of Curvilinear Coordinates, Separation of the Variables and Exact Solutions

A. V. Ivaskkevich, P. O. Sachenok, E. M. Ovsiyuk and V. M. Red'kov

This paper addresses the problem of separation of variables in quantum mechanical equations. Building on known results for the Laplace and Schroedinger equations in Euclidean space, we extend task to the Pauli equation. An explicit covariant form of the Pauli equation is derived for twelve orthogonal coordinate systems, and a unified method for handling these systems is proposed. Within the framework of the theory of relativistic quantum mechanical wave equations, in non-relativistic limit and in the first-order formalism, we propose a new algebraic approach to separation of variables. Several examples are presented to demonstrate complete separation and the effective applicability of the method.

Key words: tetrad formalism, Pauli equation, Euclidean 3-space, curvilinear coordinate systems, first order formalism, separation of the variables, exact solutions

DOI: https://doi.org/10.5281/zenodo.21104545

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