Exact Time-Dependent Wave Functions of a Confined Time-Dependent Harmonic Oscillator with Two Moving Boundaries

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Communications in Theoretical Physics ›› 2009, Vol. 52 ›› Issue (05) : 820-824.

C.F. Lo

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Abstract

By applying the standard analytical techniques of solving partial differential equations, we have obtained the exact solution in terms of the Fourier sine series to the time-dependent Schrödinger equation describing a quantum one-dimensional harmonic oscillator of time-dependent frequency confined in an infinite square well with the two walls moving along some parametric trajectories. Based upon the orthonormal basis of quasi-stationary wave functions, the exact propagator of the system has also been analytically derived. Special cases like (i) a confined free particle, (ii) a confined time-independent harmonic oscillator, and (iii) an aging oscillator are examined, and the corresponding time-dependent wave functions are explicitly determined. Besides, the approach has been extended to solve the case of a confined generalized time-dependent harmonic oscillator for some
parametric moving boundaries as well.

Key words

infinite square well / harmonic oscillator / moving boundaries / Fourier series

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C.F. Lo. Exact Time-Dependent Wave Functions of a Confined Time-Dependent Harmonic Oscillator with Two Moving Boundaries[J]. Communications in Theoretical Physics, 2009, 52(05): 820-824