Progress of Theoretical Physics
Supplement No.150 (2003) pp. 37-47
URL : http://ptp.ipap.jp/link?PTPS/150/37/
DOI : 10.1143/PTPS.150.37

Basic Analogs of Schrödinger's Equation

Kristine Ey^* and Andreas Ruffing^**

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.

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

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