Generalization of the Darboux transformation and generalized harmonic oscillators

Details Generalization of the Darboux transformation and generalized harmonic oscillators Generalization of the Darboux transformation and generalized harmonic oscillators

2003-05-28

arxiv.org/abs/quant-ph/0305174v1

J. Phys. A: Math. Gen. 36 (15 August 2003) 8673-8684

Physics

Quantum Physics

Scientific paper

10.1088/0305-4470/36/32/308

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.

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