Exact Quantized Momentum Eigenvalues and Eigenstates of a General Potential Model

TL;DR

This paper derives exact quantized momentum eigenvalues and eigenstates for a general potential in the Feinberg-Horodecki equation, illustrating with specific time-dependent potentials and analyzing their behavior graphically.

Contribution

It provides a general analytical solution for momentum eigenvalues and states in the time-dependent Feinberg-Horodecki equation for a broad class of potentials.

Findings

Explicit formulas for momentum eigenvalues and states for the general potential.

Illustrative examples with Wei-Hua Oscillator and Manning-Rosen potentials.

Graphical analysis of potential variations and momentum states.

Abstract

We obtain the quantized momentum eigenvalues, $P_n$ , and the momentum eigenstates for the space-like Schr\"odinger 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.