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Generalization of the Darboux transformation and generalized harmonic oscillators

Dae-Yup Song1,2 and John R Klauder3

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The Darbroux transformation is generalized for time-dependent Hamiltonian systems which include a term linear in momentum and a time-dependent mass. The formalism for the N-fold application of the transformation is also established, and these formalisms are applied for a general quadratic system (a generalized harmonic oscillator) and a quadratic system with an inverse-square interaction up to N = 2. Among the new features found, it is shown, for the general quadratic system, that the shape of potential difference between the original system and the transformed system could oscillate according to a classical solution, which is related to the existence of coherent states in the system.


PACS

03.65.Ge Solutions of wave equations: bound states

MSC

81R30 Coherent states (See also 22E45); squeezed states (See also 81V80)

35Q05 Euler-Poisson-Darboux equation and generalizations

Subjects

Quantum information and quantum mechanics

Dates

Issue 32 (15 August 2003)

Received 29 May 2003

Published 29 July 2003



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