The damped Pinney equation and its applications to dissipative quantum mechanics

Details The damped Pinney equation and its applications to dissipative quantum mechanics The damped Pinney equation and its applications to dissipative quantum mechanics

2007-12-25

arxiv.org/abs/0712.4083v3

Physics

Mathematical Physics

6 figures

Scientific paper

The work considers the damped Pinney equation, defined as the model arising when a linear in velocity damping term is included in the Pinney equation. In the general case the resulting equation does not admit Lie point symmetries or is reducible to a simpler form by any obvious coordinate transformation. In this context the method of Kuzmak-Luke is applied to derive a perturbation solution, for weak damping and slow time-dependence of the frequency function. The perturbative and numerical solutions are shown to be in good agreement. The results are applied to examine the time-evolution of Gaussian shaped wave-functions in the Kostin formulation of dissipative quantum mechanics.

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