The Time Inversion for Modified Oscillators

Details The Time Inversion for Modified Oscillators The Time Inversion for Modified Oscillators

2008-08-22

arxiv.org/abs/0808.3149v9

Physics

Mathematical Physics

33 pages, four figures, and two tables

Scientific paper

We discuss a new completely integrable case of the time-dependent Schroedinger equation in $R^n$ with variable coefficients for a modified oscillator, which is dual with respect to the time inversion to a model of the quantum oscillator recently considered by Meiler, Cordero-Soto, and Suslov. A second pair of dual Hamiltonians is also found in the momentum representation. Our examples show that in mathematical physics and quantum mechanics a change in the direction of time may require a total change of the system dynamics in order to return the system back to its original quantum state. Particular solutions of the corresponding Schroedinger equations are also obtained. A Hamiltonian structure of the classical integrable problem and its quantization are also discussed.

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