Three-Dimensional Matrix Superpotentials
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...
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| Date: | 2012 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2012
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/2688 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | 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. |
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