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Canadian Journal of Physics

Nonrelativistic Shannon information entropy for Killingbeck potential

Amene Najafizade, HASSAN HASSANABADI, S. Zarrinkamar

Published Aug 16, 2016• 21 citations
Publisher

Abstract

The Shannon entropy of a nonrelativistic quantum system is investigated with the Killingbeck potential, which includes Coulomb, linear, and harmonic terms. The position and momentum information entropies for the low-lying states n = 0, 1 are calculated. Some interesting features of the information entropy densities as well as the probability densities are demonstrated. The Bialynicki-Birula–Mycielski inequality is checked regarding the results.

DOI
10.1139/cjp-2016-0113

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The Shannon entropy of a nonrelativistic quantum system is investigated with the Killingbeck potential, which includes Coulomb, linear, and harmonic terms. The position and momentum information entropies for the low-lying states n = 0, 1 are calculated. Some interesting features of the information entropy densities as well as the probability densities are demonstrated. The Bialynicki-Birula–Mycielski inequality is checked regarding the results.
The exact solutions to the Schrödinger equation with a hyperbolic potential are obtained. The position S x and momentum S p Shannon information entropies for the low-lying states are calculated. Some interesting features of the information entropy densities and as well as the probability densities and are demonstrated. We find that the choices of the values for those parameters have to satisfy the condition on . We also notice that the and are symmetric to the momentum p and the or is equal or greater than 1 at some positions r or momentum p . In addition, the Bialynicki-Birula–Mycielski inequality is tested from different cases and found to hold for these cases.
In this paper, we studied, at first, the influence of the energy-dependent potentials on the one-dimensionless Klein–Gordon oscillator. Then, the Shannon entropy and Fisher information of this system are investigated. The position and momentum information entropies for the low-lying states n = 0, 1, 2 are calculated. Some interesting features of both Fisher and Shannon densities, as well as the probability densities, are demonstrated. Finally, the Stam, Cramer–Rao and Bialynicki–Birula–Mycielski (BBM) inequalities have been checked, and their comparison with the regarding results have been reported. We showed that the BBM inequality is still valid in the form [Formula: see text], as well as in ordinary quantum mechanics.
Shannon entropy for the position and momentum eigenstates of the symmetrically trigonometric Rosen–Morse potential for the lower states n = 1–4 is evaluated. The position information entropies S x for n = 1,2 are presented analytically. Some interesting features of the information entropy densities ρ s ( x ) and ρ s ( p ) are demonstrated graphically. We find that the ρ s ( p ) is inversely proportional to the range of potential a and the S x decreases with increasing the potential depth D . In particular, we note that the S x might become negative for some given parameters a and D . The Bialynicki-Birula–Mycielski inequality is also tested for a number of states and is found to generally hold well.
Abstract Shannon entropy for the position and momentum eigenstates of an asymmetric trigonometric Rosen–Morse potential for the ground and first excited states is evaluated. The position and momentum information entropies and are calculated numerically. Also, it is found that is obtained analytically and increases with the potential depth and width. Some interesting features of the information entropy densities and are demonstrated graphically. The Bialynicki‐Birula–Mycielski inequality is also tested and found to hold good.