Abstract
A simple and algorithmic description of additive shape invariant matrix potentials is presented. The dependence of the corresponding superpotentials on the variable parameter κ is restricted to linear combinations of powers κν with ν = 0, 1, −1. The complete lists of matrix superpotentials of dimensions 2 × 2 and of special superpotentials of dimensions 3 × 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 shape invariant systems of coupled Schrödinger equation is classified. Examples of such systems are considered in detail. New multidimensional models which can be reduced to shape invariant systems via separation of variables are presented.
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