Feinberg-Horodocki exact momentum states of improved deformed exponential-type potential (original) (raw)
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Feinberg-Horodecki Exact Momentum States of Improved Deformed Exponential-Type Potential
Journal of Applied Mathematics and Physics, 2020
We obtain the quantized momentum eigenvalues, P n , and the momentum eigenstates for the space-like Schrodinger equation, the Feinberg-Horodecki equation, with the improved deformed exponential-type potential which is constructed by temporal counterpart of the spatial form of these potentials. We also plot the variations of the improved deformed exponentialtype potential with its momentum eigenvalues for few quantized states against the screening parameter.
Exact Quantized Momentum Eigenvalues and Eigenstates of a General Potential Model
Journal of Applied Mathematics and Physics, 2020
We obtain the quantized momentum eigenvalues, n P , and the momentum eigenstates for the space-like Schrödinger equation, the Feinberg-Horodecki equation, with the general potential which is constructed by the temporal counterpart of the spatial form of these potentials. The present work is illustrated with two special cases of the general form: time-dependent Wei-Hua Oscillator and time-dependent Manning-Rosen potential. We also plot the variations of the general molecular potential with its two special cases and their momentum states for few quantized states against the screening parameter.
Journal of Applied Mathematics and Physics, 2020
We obtain an approximate value of the quantized momentum eigenvalues, P n , together with the space-like coherent eigenvectors for the space-like counterpart of the Schrdinger equation, the Feinberg-Horodecki equation, with a screened Kratzer-Hellmann potential which is constructed by the temporal counterpart of the spatial form of this potential. In addition, we got exact eigenvalues of the momentum and the eigenstates by solving Feinberg-Horodecki equation with Kratzer potential. The present work is illustrated with three special cases of the screened Kratzer-Hellman potential: the time-dependent screened Kratzer potential, timedependent Hellmann potential and, the time-dependent screened Coulomb potential.
Exact analytic solutions of the Schrödinger equations for some modified q-deformed potentials
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In this paper, we introduce the exact solution for the wave function in the presence of potential energy, consisting of combination between q-deformed hyperbolic and exponential function with different argument. The functions we have used in the present communication can be regarded as a generalization of the Arai q-deformed function (modified q-deformed Morse potential). In this context, we have restricted our discussion for some particular cases of the q-deformed hyperbolic functions. This is due to the difficulty for dealing with most of the arguments included in the potential functions. For the most particular cases, the energy eigenfunctions are obtained, and the behavior is also discussed. It has been shown that the wave functions are sensitive to the variation in the value of q-deformed parameter as well as the strength of the potential parameter k. Furthermore, the energy eigenvalues are also considered for some particular cases where the argument of the exponential function plays a strong role effecting its value.
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Feinberg-Horodecki Equation with Pöschl-Teller Potential: Space-like Coherent States
Zeitschrift für Naturforschung A
We obtain the quantized momentum solutions, Pn, 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.
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The major of physics applications of quantum mechanics is based on the Schrödinger equation, it was most successful in describing physics phenomena’s in 2 and 3 dimensional spaces and in a particular in the central potentials at week energy to study the atoms nuclei, molecules and their spectral behaviours, this theory will correctly described phenomena only when the velocities are small compared to the light [1-19]. The second revolution in the last century it was the standard model, in where the three fundamental forces in nature: electromagnetic, week and strong, are successful unfitted in the framework of gauge field theories. But the last forth forces, gravitation, its out of this model of unification. The hop to get a new gauge theory, in which the four forces at include in this theory, is possible, when the symmetries will be huge, which satisfied by the notion of the noncommutativity of space-time, which is extended to the canonical commutation relations between position coo...
Constraints and spectra of a deformed quantum mechanics
Physical Review D, 2012
We examine a deformed quantum mechanics in which the commutator between coordinates and momenta is a function of momenta. The Jacobi identity constraint on a two-parameter class of such modified commutation relations (MCR's) shows that they encode an intrinsic maximum momentum; a sub-class of which also imply a minimum position uncertainty. Maximum momentum causes the bound state spectrum of the one-dimensional harmonic oscillator to terminate at finite energy, whereby classical characteristics are observed for the studied cases. We then use a semi-classical analysis to discuss general concave potentials in one dimension and isotropic power-law potentials in higher dimensions. Among other conclusions, we find that in a subset of the studied MCR's, the leading order energy shifts of bound states are of opposite sign compared to those obtained using stringtheory motivated MCR's, and thus these two cases are more easily distinguishable in potential experiments.
On Quantization, the Generalized Schrödinger Equation and Classical Mechanics
UM-P-91/47, 1991
Using a new state-dependent, λ-deformable, linear functional operator, Q λ ψ , which presents a natural C ∞ deformation of quantization, we obtain a uniquely selected non-linear, integro-differential Generalized Schrödinger equation. The case Q 1 ψ reproduces linear quantum mechanics, whereas Q 0 ψ admits an exact dynamic, energetic and measurement theoretic reproduction of classical mechanics. All solutions to the resulting classical wave equation are given and we show that functionally chaotic dynamics exists.