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Quasi-coherent states for harmonic oscillator with time-dependent parameters. (English) Zbl 1273.81086
Summary: In this study, we discuss the harmonic oscillator with the time-dependent frequency, \(\omega(t)\), and the mass, \(M(t)\), by generalizing the holomorphic coordinates for the harmonic oscillator. In general cases, we solve the Schrödinger equation by reducing it into the Riccati equation and discuss the uncertainties for the quasi-coherent states of the time-dependent harmonic oscillator. In special cases, we find the following results: First, for a time-dependent harmonic oscillator, if [\(\omega(t)M(t)\)] is constant, then the coherent states will evolve as the coherent states. Second, for the driven harmonic oscillator, the coherent states will evolve as the coherent states with new eigenvalues. Third, we derive quasi-coherent states for the Caldirola-Kanai Hamiltonian and show that the product of uncertainties, \(\Delta x \Delta p\), is larger than minimum value; however, it is constant. We also discuss the classical equations of motion for the system.
©2012 American Institute of Physics

MSC:
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81R30 Coherent states
35Q41 Time-dependent Schrödinger equations and Dirac equations
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
70K25 Free motions for nonlinear problems in mechanics
70K40 Forced motions for nonlinear problems in mechanics
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