
Symmetry and Integrability of Equations of Mathematical Physics − 2011
Yuri Karadzhov (Institute of Mathematics of NAS of Ukraine, Kyiv, Ukraine)
Matrix Superpotentials
Abstract:
The classification of matrixvalued shapeinvariant
super potentials which give rise to new exactly solvable systems of
Schrödinger equations is presented. The superpotentials of the
generic form $W_k = kQ + P +\frac1k R$, where $k$ is variable
parameter, $P, Q$ and $R$ are hermitian matrices of an arbitrary
dimension $n$, are considered. Additionally it supposed that matrices
$P, Q$ and $R$ are not zero matrices and they are not proportional to
the unit matrix.

