Generic matrix superpotentials

Abstract

A simple and algorithmic description of matrix shape invariant potentials is presented. The complete lists of generic matrix superpotentials of dimension $2\times 2$ and of special superpotentials of dimension $3\times 3$ are given explicitly. In addition, a constructive description of superpotentials realized by matrices of arbitrary dimension is presented. In this way an extended class of integrable systems of coupled Schrödinger equation is classified. Examples of such systems are considered in detail. New integrable multidimensional models which are reduced to shape invariant systems via separation of variables are presented also.

Ref. 17 is added

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Cited by in corpus (8)

• Symmetries and solutions of field equations of axion electrodynamics
• Integrability and supersymmetry of Schroedinger-Pauli equations for neutral particles
• Laplace-Runge-Lenz vector for arbitrary spin
• Symmetries of Schroedinger equation with scalar and vector potentials
• Minimal Realizations of Supersymmetry for Matrix Hamiltonians
• Symmetries of the Schroedinger-Pauli equation for neutral particles
• Applications of the potential algebras of the two-dimensional Dirac-like operators
• Supersymmetric Quantum Mechanics, Engineered Hierarchies of Integrable Potentials, and the Generalised Laguerre Polynomials