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Prog. Theor. Phys. Supplement No.150 (2003) pp. 37-47

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Basic Analogs of Schrödinger's Equation

Kristine Ey* and Andreas Ruffing**

Munich University of Technology, Dept. of Mathematics,
Boltzmannstraße 3, D-85747 Garching, Germany

Abstract:

Basic analogs of Schrödinger's equation are investigated on a so-called q-linear grid or basic linear grid. A ladder operator formalism for a discrete harmonic oscillator analog is developed with a representation in the weighted Hilbert space l2(\BbbZ) over the q-linear grid. The moment problem for the corresponding modified discrete q-Hermite polynomials of type II is revised. Conditions on the existence of a ladder operator formalism in connection with the considered moment problem are developed. The results are evaluated with respect to an application for purposes of discrete Schrödinger theory.


URL : http://ptp.ipap.jp/link?PTPS/150/37/
DOI : 10.1143/PTPS.150.37


*E-mail: ey@appl-math.tu-muenchen.de
**E-mail: ruffing@ma.tum.de

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References:

  1. R. Askey and S. K. Suslov, J. of Phys. A 26 (1993), 693[IoP STACKS].
  2. R. Askey and S. K. Suslov, Lett. Math. Phys. 29 (1993), 123.
  3. C. Berg and M. E. H. Ismail, Can. J. Math. 48 (1996), 43.
  4. C. Berg, J. Comput. Appl. Math. 99 (1998), 67.
  5. C. Berg and A. Ruffing, Commun. Math. Phys. 223 (2001), 29[CrossRef].
  6. L. Biedenharn, J. of Phys. A 26 (1993), L873[IoP STACKS].
  7. K. Ey and A. Ruffing, accepted for publication in Dyn. Sys. and Appl. 12.
  8. A. Hebecker, S. Schreckenberg, J. Schwenk, W. Weich and J. Wess, Z. Phys. C 64 (1994), 355.
  9. M. E. H. Ismail and M. Rahman, J. Math. Anal. Appl. 218 (1998), 155.
  10. T. Kato, Perturbation Theory for Linear Operators (Springer, Berlin, Heidelberg, New York, 1995).
  11. E. Koelink and J. V. Stokman, in Special Functions 2000: Current Perspective and Future Directions, ed. J. Bustoz, M. E. H. Ismail and S. K.  Suslov (NATO Science Series II, 30, Kluwer, 2001).
  12. E. Koelink and J. V. Stokman, to appear in Constr. Approx., see math.CA/9904111.
  13. A. Lorek, A. Ruffing and J. Wess, Z. Phys. C 74 (1997), 369.
  14. A. Macfarlane, J. of Phys. A 22 (1993), 4581[IoP STACKS].
  15. D. R. Masson and J. Repka, SIAM J. Math. Anal. 22 (1991), 1131.
  16. K. A. Penson and A. I. Solomon, J. Math. Phys. 40 (1999), 2354[AIP Scitation].
  17. A.  Ruffing, Prog. Theor. Phys. Suppl. No. 139 (2000), 404[IPAP].
  18. K. Schmüdgen, Unbounded operator algebras and representation theory (Akademie-Verlag, Berlin, Birkhäuser-Verlag, Basel, 1990).
  19. S. K. Suslov, Developments in Mathematics 9 (Kluwer series, 2003).
  20. S. K. Suslov, in Special Functions 2000: Current Perspective and Future Directions, ed. J. Bustoz, M. E. H. Ismail and S. K. Suslov (NATO Science Series II, 30, Kluwer, 2001), p. 411.

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