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The Darboux-like transform and some integrable cases of the q-Riccati equation

Anatol Odzijewicz and Alina Ryzko

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Using the q-version of the Darboux transform we obtain the general solution of  q-difference Riccati equation from a special one by the action of one-parameter group. This allows us to construct the solutions for the large class of  q-difference Riccati equations as well as q-difference Schrödinger equations, which are different from those obtained by the standard Darboux transform.


PACS

02.30.Uu Integral transforms

03.65.Ge Solutions of wave equations: bound states

MSC

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other quantum-mechanical equations

44A05 General transforms (See also 42A38)

Subjects

Mathematical physics

Quantum information and quantum mechanics

Dates

Issue 3 (25 January 2002)

Received 20 July 2001, in final form 24 October 2001

Published 11 January 2002



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