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Register a new userFeinberg-Horodecki Equation with Poschl-Teller Potential: Space-like Coherent States
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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 Schrodinger equation with trigonometric Poschl-Teller potential which is constructed by temporal counterpart of the spatial Poschl-Teller potential.
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We obtain the quantized momentum eigenvalues, $P_n$, together with space-like coherent eigenstates for the space-like counterpart of the Schru007fodinger equation, the Feinberg-Horodecki equation, with a combined Kratzer potential plus screened coulomb potential which is constructed by temporal counterpart of the spatial form of these potentials. The present work is illustrated with two special cases of the general form: the time-dependent modified Kratzer potential and the time-dependent screened Coulomb potential.
The solution of the Feinberg-Horodecki (FH) equation for a time-dependent mass (TDM) harmonic oscillator quantum system is studied. A certain interaction is applied to a mass to provide a particular spectrum of stationary energies. The related spectrum of the harmonic oscillator potential acting on the TDM oscillators is found. We apply the time version of the asymptotic iteration method (AIM) to calculate analytical expressions of the TDM stationary state energies and their wave functions. It is shown that the obtained solutions reduce to those of simple harmonic oscillator as the time-dependent of the mass reduces to
The energy eigenvalues and the corresponding eigenfunctions of the one-dimensional Klein-Gordon equation with q-parameter Poschl-Teller potential are analytically obtained within the position-dependent mass formalism. The parametric generalization of the Nikiforov-Uvarov method is used in the calculations by choosing a mass distribution.
The quantum phase-space dynamics driven by hyperbolic Poschl-Teller (PT) potentials is investigated in the context of the Weyl-Wigner quantum mechanics. The obtained Wigner functions for quantum superpositions of ground and first-excited states exhibit some non-classical and non-linear patterns which are theoretically tested and quantified according to a non-gaussian continuous variable framework. It comprises the computation of quantifiers of non-classicality for an anharmonic two-level system where non-Liouvillian features are identified through the phase-space portrait of quantum fluctuations. In particular, the associated non-gaussian profiles are quantified by measures of {em kurtosis} and {em negative entropy}. As expected from the PT {em quasi}-harmonic profile, our results suggest that quantum wells can work as an experimental platform that approaches the gaussian behavior in the investigation of the interplay between classical and quantum scenarios. Furthermore, it is also verified that the Wigner representation admits the construction of a two-particle bipartite quantum system of continuous variables, $A$ and $B$, identified by $sum_{i,j=0,1}^{i eq j}vert i_{_A}rangleotimesvert j_{_B}rangle$, which are shown to be separable under gaussian and non-gaussian continuous variable criteria.
We analyze the one dimensional scattering produced by all variations of the Poschl-Teller potential, i.e., potential well, low and high barriers. We show that the Poschl-Teller well and low barrier potentials have no resonance poles, but an infinite number of simple poles along the imaginary axis corresponding to bound and antibound states. A quite different situation arises on the Poschl-Teller high barrier potential, which shows an infinite number of resonance poles and no other singularities. We have obtained the explicit form of their associated Gamow states. We have also constructed ladder operators connecting wave functions for bound and antibound states as well as for resonance states. Finally, using wave functions of Gamow and antibound states in the factorization method, we construct some examples of supersymmetric partners of the Poschl-Teller Hamiltonian.
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