Spectral measure function separability and reflectionless potentials

  • Authors

    • Eric A. Kincanon Gonzaga University
    2018-07-26
    https://doi.org/10.14419/ijamr.v7i3.9898
  • Inverse Scattering, Reflection less Potentials.

  • Both reflectionless potentials and special conditions on the spectral measure function have been well studied in inverse scattering theory. This short paper considers a spectral measure function that is separable and shows that it is equivalent to the potential being reflectionless.

     

     

     

     

  • References

    1. [1] I.M. Gelfand, B.M. Levitan, on the determination of a differential equation by its spectral function, Dokl. Akad. Nauk. USSR 77 (1951) 557-560.

      [2] I.M. Gelfand, B.M. Levitan, on the determination of a differential equation by its spectral measure function, Izv. Akad. Nauk. SSR 15 (1951) 309-360.

      [3] K. Chadan, P.C. Sabatier, Inverse Problems in Quantum Scattering Theory, Springer-Verlag, NewYork, 1977. https://doi.org/10.1007/978-3-662-12125-2.

      [4] R. Jost, W. Kohn, on the relation between phase shift energy levels and the potential, Danske Vid. Selsk. Math. Fys. 27 (1953) 3-19.

      [5] J. Lekner, Reflectionless eigenstates of the sech2 potential, Am. J. Phys. 75 (2007) 1151-1157. https://doi.org/10.1119/1.2787015.

      [6] E. Kincanon, An Orthogonal Set Composed from the Functions enx, Applied Mathematics and Computation, 41, (1991) 69-75. https://doi.org/10.1016/0096-3003(91)90107-X.

      [7] E. Kincanon, Approximate solution to the Gelfand-Levitan equation, Applied Mathematics and Computation, 53 (1993) 121-128. https://doi.org/10.1016/0096-3003(93)90097-X.

      [8] E. Kincanon, Spectral measure function separability and reflectionless potentials, Applied Mathematics and Computation, 123 (2001) 409-412. https://doi.org/10.1016/S0096-3003(00)00086-2.

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  • How to Cite

    A. Kincanon, E. (2018). Spectral measure function separability and reflectionless potentials. International Journal of Applied Mathematical Research, 7(3), 69-70. https://doi.org/10.14419/ijamr.v7i3.9898