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arXiv:2007.13836 · Journal of Applied Mathematics and Physics

Exact Quantized Momentum Eigenvalues and Eigenstates of a General Potential Model

Mahmoud Farout, Ahmed Bassalat, Sameer M. Ikhdair

Published Jan 1, 2020• 11 citations
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Abstract

We obtain the quantized momentum eigenvalues, Pn, and the momentum eigenstates for the space-like Schr?dinger 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.

DOI
10.4236/jamp.2020.87109

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We obtain an approximate value of the quantized momentum eigenvalues, Pn, together with the space-like coherent eigenvectors for the space-like counterpart of the Schrödinger 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, time-dependent Hellmann potential and, the time-dependent screened Coulomb potential.
We obtain the quantized momentum eigenvalues Pn together with space-like coherent eigenstates for the space-like counterpart of the Schrödinger 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.
In this study, we obtained exact solutions of the Feinberg–Horodecki equation for the time-dependent Wei-Hua potential, which is constructed by the temporal counterpart of the spatial form of this potential. We obtained the quantized momentum eigenvalues and the corresponding wave functions. We obtained the partition function for the system and studied other thermodynamic properties that include vibrational mean momentum ( U), vibrational specific heat capacity ( C), vibrational entropy ( s), and vibrational free momentum ( F) as a signature in the momentum space.