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Matrix Superpotentials of Special Form

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We present a classification of matrix superpotentials corresponding to exactly solvable Schrödinger equations and consider superpotentials of a special form \( {W}_k=kQ+\frac{1}{k}R \), where k is a parameter, P and R are Hermitian matrices depending on the variable x. The list of two-dimensional matrix potentials is presented in the explicit form.

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References

  1. E. Witten, “Dynamical breaking of supersymmetry,” Nucl. Phys. B, 185, No. 513 (1981).

  2. L. Gendenshtein, “Derivation of exact spectra of the Schr¨odinger equation by means of supersymmetry,” JETP Lett., 38, 356–359 (1983).

    Google Scholar 

  3. F. Cooper, A. Khare, and U. Sukhatme, “Supersymmetry and quantum mechanics,” Phys. Rep., 251, No. 5–6, 267–385 (1995).

    Article  MathSciNet  Google Scholar 

  4. G. P. Pron’ko and Y. G. Stroganov, “New example of quantum-mechanical problem with hidden symmetry,” Sov. Phys. JETP, 45, No. 5, 1075–1078 (1977).

    Google Scholar 

  5. A. I. Voronin, “Neutron in the magnetic field of a linear conductor with current as an example of the two-dimensional supersymmetric problem,” Phys. Rev. A, 43, No. 1, 29–34 (1991).

    Article  Google Scholar 

  6. L. V. Hau, G. A. Golovchenko, and M. M. Burns, “Supersymmetry and the binding of a magnetic atom to a filamentary current,” Phys. Rev. Lett., 74, No. 16, 3138–3140 (1995).

    Article  Google Scholar 

  7. E. Ferraro, N.Messina, and A. G. Nikitin, “Exactly solvable relativistic model with the anomalous interaction,” Phys. Rev. A, 81, No. 4 (2010).

  8. V. M. Tkachuk and P. Roy, “Motion of a spin-1=2 particle in shape invariant scalar and magnetic fields,” J. Phys. A, 33, No. 22, 4159–4167 (2000).

    Article  MATH  MathSciNet  Google Scholar 

  9. A. A. Andrianov, M. V. Ioffe, V. P. Spiridonov, and L. Vinet, “Parasupersymmetry and truncated supersymmetry in quantum mechanics,” Phys. Lett. B, 272, No. 3–4, 297–304 (1991).

    Article  MathSciNet  Google Scholar 

  10. A. A. Andrianov, F. Cannata, M. V. Ioffe, and D. N. Nishnianidze, “Matrix Hamiltonians: SUSY approach to hidden symmetries,” J. Phys. A, 30, No. 14, 5037–5050 (1997).

    Article  MATH  MathSciNet  Google Scholar 

  11. R. de Lima Rodrigues, V. B. Bezerra, and A. N. Vaidya, “An application of super symmetric quantum mechanics to a planar physical system,” Phys. Lett. A, 287, No. 1–2, 45–49 (2001).

    Article  MATH  Google Scholar 

  12. A. G. Nikitin and Yu. Karadzhov, “Matrix superpotentials,” J. Phys. A: Math. Theor., 44, No. 30 (2011).

  13. Yu. Karadzhov, “Matrix superpotential linear in variable parameter,” Comm. Nonlin. Sci. Numer. Simul., 17, No. 4, 1522–1528 (2012).

    Article  MATH  MathSciNet  Google Scholar 

  14. A. G. Nikitin and Yu. Karadzhov, “Enhanced classification of matrix superpotentials,” J. Phys. A: Math. Theor., 44, No. 44 (2011).

  15. Yu. A. Karadzhov, “Three-dimensional matrix superpotentials,” Ukr. Mat. Zh., 64, No. 12, 1641–1653 (2012); English translation: Ukr. Math. J., 64, No. 12, 1851–1864 (2012).

    Article  MathSciNet  Google Scholar 

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Correspondence to Yu. A. Karadzhov.

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Translated from Neliniini Kolyvannya, Vol. 16, No. 4, pp. 496–501, October–December, 2013.

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Karadzhov, Y.A. Matrix Superpotentials of Special Form. J Math Sci 203, 344–349 (2014). https://doi.org/10.1007/s10958-014-2136-0

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  • DOI: https://doi.org/10.1007/s10958-014-2136-0

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