Group Theoretical Approach to the Coherent and the Squeeze States of a Time-Dependent Harmonic Oscillator with a Singular Term
نویسندگان
چکیده
For a time-dependent harmonic oscillator with an inverse squared singular term, we find the generalized invariant using the Lie algebra of SU(2) and construct the number-type eigenstates and the coherent states using the spectrum-generating Lie algebra of SU(1, 1). We obtain the evolution operator in both of the Lie algebras. The number-type eigenstates and the coherent states are constructed group-theoretically for both the time-independent and the time-dependent harmonic oscillators with the singular term. It is shown that the squeeze operator transforms unitarily the time-dependent basis of the spectrum-generating Lie algebra of SU(1, 1) for the generalized invariant, and thereby evolves the initial vacuum into a final coherent vacuum. Typeset using REVTEX 1
منابع مشابه
Gazeau- Klouder Coherent states on a sphere
In this paper, we construct the Gazeau-Klauder coherent states of a two- dimensional harmonic oscillator on a sphere based on two equivalent approaches. First, we consider the oscillator on the sphere as a deformed (non-degenerate) one-dimensional oscillator. Second, the oscillator on the sphere is considered as the usual (degenerate) two--dimensional oscillator. Then, by investigating the quan...
متن کاملEvolution of Gaussian Wave Packet and Nonadiabatic Geomet- rical Phase for the time-dependent Singular Oscillator
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...
متن کاملSuper algebra and Harmonic Oscillator in Anti de Sitter space
The harmonic oscillator in anti de Sitter space(AdS) is discussed. We consider the harmonic oscillator potential and then time independent Schrodinger equation in AdS space. Then we apply the supersymmetric Quantum Mechanics approach to solve our differential equation. In this paper we have solved Schrodinger equation for harmonic oscillator in AdS spacetime by supersymmetry approach. The shape...
متن کاملQuantum singular oscillator as a model of two-ion trap: an amplification of transition probabilities due to small time variations of the binding potential
Following the paper by M. Combescure [Ann. Phys. (NY) 204, 113 (1990)], we apply the quantum singular time dependent oscillator model to describe the relative one dimensional motion of two ions in a trap. We argue that the model can be justified for low energy excited states with the quantum numbers n ≪ nmax ∼ 100, provided that the dimensionless constant characterizing the strength of the repu...
متن کاملNumerical Solution of the Controlled Harmonic Oscillator by Homotopy Perturbation Method
The controlled harmonic oscillator with retarded damping, is an important class of optimal control problems which has an important role in oscillating phenomena in nonlinear engineering systems. In this paper, to solve this problem, we presented an analytical method. This approach is based on the homotopy perturbation method. The solution procedure becomes easier, simpler and mor...
متن کامل