We present a construction of semi-classical states for Pöschl-Teller potentials based on a supersymmetric quantum mechanics approach. The parameters of these "coherent" states are points in the classical phase space of these systems. They minimize a special uncertainty relation. Like standard coherent states they resolve the identity with a uniform measure. They permit to establish the correspondence (quantization) between classical and quantum quantities. Finally, their time evolution is localized on the classical phase space trajectory.
New SUSYQM coherent states for Poschl-Teller potentials: a detailed mathematical analysis
在最近的一篇短文[Bergeron H，Gazeau J P，Siegl P and Youssef A 2010 EPL 92 60003]中，我们提出了一个新的Pöschl-Teller势半经典态族的良好性质。这些状态是从超对称量子力学方法建立的，这些“相干”状态的参数是经典相空间中的点。在这篇文章中，我们开发了所有的数学方面，已经离开了前一篇文章（证明决议的统一，详细计算的量化版本的经典可观的和数学研究所产生的运营商：问题的域，自伴或自伴扩展）。还研究了一些附加的渐近性态问题。此外，该框架被扩展到更大的一类Pöschl-Teller势。
We obtain the quantized momentum solutions, $\mathcal{P}_{n}$, of the Feinberg-Horodecki equation. We study the space-like coherent states for the space-like counterpart of the Schrödinger equation with trigonometric Pöschl-Teller potential which is constructed by temporal counterpart of the spatial Pöschl-Teller potential.
We introduce a generalization structure of the su(1,1) algebra which depends on a function of one generator of the algebra, f(H). Following the same ideas developed to the generalized Heisenberg algebra (GHA) and to the generalized su(2), we show that a symmetry is present in the sequence of eigenvalues of one generator of the algebra. Then, we construct the Barut-Girardello coherent states associated with the generalized su(1,1) algebra for a particle in a Pöschl-Teller potential. Furthermore, we compare the time evolution of the uncertainty relation of the constructed coherent states with th…
构造一类精确可解势的相干态的一般代数方法，Morse和P{<$}schl-Teller，给出。该方法{ \it a priori}是势函数无关的，并与先前发展的方法，包括基于振子的相干态方法及其推广相联系。这种方法可以直接推广到构造更一般的量子力学势问题的相干态，如振子的非线性相干态。这些相干态的时间演化特性，显示复苏和分数复苏，表现在自相关函数，以及，在量子地毯结构。
We obtained analytical expressions for Entangled of Formation (EoF) and Quantum Discord (QD) of Werner states and Generalized Werner-Like states. The optimization problem involved under the exact analytical form is obtained for both quantities. In order to illustrate the importance of our results we studied the EoF and the QD of these states. Using discrete formulation of continue states with the $f-$deformed coherent states obtained as deformed annihilation operator coherent states and as deformed displacement operator coherent states. The EoF and QD of bipartite Werner-Like states $f-$deform…
We apply geometric phase ideas to coherent states to shed light on interference phenomenon in the phase space description of continuous variable Cartesian quantum systems. In contrast to Young's interference characterized by path lengths, phase space interference turns out to be determined by areas. The motivating idea is Pancharatnam's concept of "being in phase" for Hilbert space vectors. Applied to the overcomplete family of coherent states, we are led to preferred one-dimensional integral representations for various states of physical significance, such as the position, momentum, Fock stat…
We introduce a group-theoretical extension of the Dicke model which describes an ensemble of two-level atoms interacting with a finite radiation field. The latter is described by a spin model whose main feature is that it possesses a maximum number of excitations. The approach adopted here leads to a nonlinear extension of the Dicke model that takes into account both an intensity dependent coupling between the atoms and the radiation field, and an additional nonlinear Kerr-like or Pösch-Teller-like oscillator term, depending on the degree of nonlinearity. We use the energy surface minimization…
