Evolution of Gaussian Wave Packet and Nonadiabatic Geomet- rical Phase for the time-dependent Singular Oscillator
نویسنده
چکیده
The geometrical phase of a time-dependent singular oscillator is obtained in the framework of Gaussian wave packet. It is shown by a simple geometrical approach that the geometrical phase is connected to the classical nonadiabatic Hannay angle of the generalized Harmonic oscillator. Explicitly time-dependent problems present special difficulties in classical and quantum mechanics. However, they deserve detailed study because very interesting properties emerge when, even for simple linear systems, some parameters are allowed to vary with time. For instance, particular recent interest has been devoted to systems in which evolution originates geometric contributions [1-6]. One of these, the generalized harmonic oscillator has invoked much attention to study the nonadiabatic geometric phase for various quantum states, such as Gaussian, number, squeezed or coherent states, which can be found exactly [7-10]. Recently, the geometric phase for a cyclic wave packet solution of the generalized harmonic oscillator and its relation
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