Three-Dimensional Matrix Superpotentials

  • Yu. A. Karadzhov Iн-т математики НАН України, Київ


We consider a special case for curves in two-, three-, and four-dimensional Euclidean spaces and obtain a necessary and sufficient condition for the tensor product surfaces of the planar unit circle centered at the origin and these curves to have a harmonic Gauss map. We present а classification of matrix superpotentials that correspond to exactly solvable systems of Schrodinger equations. Superpotentials of the following form are considered: $W_k = kQ + P \frac 1k$, where $k$ is a parameter and $P, Q$ and $R$ are Hermitian matrices that depend on a variable $x$. The list of three-dimensional matrix superpotentials is explicitly presented.
How to Cite
Karadzhov, Y. A. “Three-Dimensional Matrix Superpotentials”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, no. 12, Dec. 2012, pp. 1641-0,
Research articles