Three-dimensional Matrix Superpotentials

This article considers the classification of matrix superpotentials that corresponds to exactly solvable systems of Schrodinger equations. Superpotentials of the following form are considered: $W_k = kQ + P + \frac1kR$, where $k$ --- parameter, $P, Q$ and $R$ --- hermitian matrices, that depend on a variable $x$. The list of three-dimensional matrix superpotentials is presented explicitly.