Abstract
We present a collection of matrix valued shape invariant potentials which give rise to new exactly solvable problems of SUSY quantum mechanics. It includes all irreducible matrix superpotentials of the generic form \(W = kQ + \frac{1} {k}R + P\) where k is a variable parameter, Q is the unit matrix multiplied by a real valued function of independent variable x, and P, R are hermitian matrices depending on x. In particular we recover the Pron’ko-Stroganov “matrix Coulomb potential” and all known scalar shape invariant potentials of SUSY quantum mechanics. In addition, five new shape invariant potentials are presented.
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Acknowledgements
The author thanks the Organizing Committee and especially Prof. Vladimir Dobrev for hospitality and giving an opportunity to give a talk. His participation in the Workshop was supported by the Abdus Salam International Centre for Theoretical Physics. The author is also grateful to Prof. Anatoly Nikitin for useful discussions and valuable comments.
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Karadzhov, Y. (2013). Matrix Superpotentials. In: Dobrev, V. (eds) Lie Theory and Its Applications in Physics. Springer Proceedings in Mathematics & Statistics, vol 36. Springer, Tokyo. https://doi.org/10.1007/978-4-431-54270-4_35
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DOI: https://doi.org/10.1007/978-4-431-54270-4_35
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