Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1103.1246 · Journal of Mathematical Physics

Information entropy of conditionally exactly solvable potentials

D. Dutta, P. Roy

Published Mar 1, 2011• 34 citations
arXivHTMLPDF

Abstract

We evaluate Shannon entropy for the position and momentum eigenstates of some conditionally exactly solvable potentials which are isospectral to harmonic oscillator and whose solutions are given in terms of exceptional orthogonal polynomials. The Bialynicki–Birula–Mycielski inequality has also been tested for a number of states.
DOI
10.1063/1.3566977

Related papers

Quantum information entropy for a hyperbolical potential function

R Valencia-Torres, Guo-Hua Sun, Shi‐Hai Dong

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.

Physica Scripta•Feb 5, 2015•76 citations

Quantum information entropies of the eigenstates for a symmetrically trigonometric Rosen–Morse potential

Guo-Hua Sun, Shi‐Hai Dong

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.

Physica Scripta•Feb 28, 2013•71 citations

Entropy of Hermite polynomials with application to the harmonic oscillator

Walter Van Assche

We analyse the entropy of Hermite polynomials and orthogonal polynomials for the Freud weights w(x)=exp(-|x|^m) on the real line and show how these entropies are related to information entropy of the one-dimensional harmonic oscillator. The physical interest in such entropies comes from a stronger version of the Heisenberg uncertainty principle, due to Bialynicki-Birula and Mycielski, which is expressed as a lower bound for the sum of the information entropies of a quantum-mechanical system in the position space and in the momentum space.

•Jan 1, 1996•1 citation

Nonrelativistic Shannon information entropy for Killingbeck potential

Amene Najafizade, HASSAN HASSANABADI, S. Zarrinkamar

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.

Canadian Journal of Physics•Aug 16, 2016•21 citations

Quantum information entropies for an asymmetric trigonometric Rosen–Morse potential

Guo-Hua Sun, Shi‐Hai Dong, Nasser Saad

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.

Annalen der Physik•Jul 22, 2013•89 citations

Quantum information entropies of the eigenstates for the Pöschl—Teller-like potential

Guo-Hua Sun, Manuél Ávila, Shi‐Hai Dong

Shannon entropy for lower position and momentum eigenstates of Pöschl—Teller-like potential is evaluated. Based on the entropy densities demonstrated graphically, we note that the wave through of the position information entropy density ρ( x ) moves right when the potential parameter V 1 increases and its amplitude decreases. However, its wave through moves left with the increase in the potential parameter | V 2 |. Concerning the momentum information entropy density ρ( p ), we observe that its amplitude increases with increasing potential parameter V 1 , but its amplitude decreases with increasing | V 2 |. The Bialynicki—Birula—Mycielski (BBM) inequality has also been tested for a number of states. Moreover, there exist eigenstates that exhibit squeezing in the momentum information entropy. Finally, we note that position information entropy increases with V 1 , but decreases with | V 2 |. However, the variation of momentum information entropy is contrary to that of the position information entropy.

Chinese Physics B•May 1, 2013•76 citations
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.
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.
We analyse the entropy of Hermite polynomials and orthogonal polynomials for the Freud weights w(x)=exp(-|x|^m) on the real line and show how these entropies are related to information entropy of the one-dimensional harmonic oscillator. The physical interest in such entropies comes from a stronger version of the Heisenberg uncertainty principle, due to Bialynicki-Birula and Mycielski, which is expressed as a lower bound for the sum of the information entropies of a quantum-mechanical system in the position space and in the momentum space.
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.
Shannon entropy for lower position and momentum eigenstates of Pöschl—Teller-like potential is evaluated. Based on the entropy densities demonstrated graphically, we note that the wave through of the position information entropy density ρ( x ) moves right when the potential parameter V 1 increases and its amplitude decreases. However, its wave through moves left with the increase in the potential parameter | V 2 |. Concerning the momentum information entropy density ρ( p ), we observe that its amplitude increases with increasing potential parameter V 1 , but its amplitude decreases with increasing | V 2 |. The Bialynicki—Birula—Mycielski (BBM) inequality has also been tested for a number of states. Moreover, there exist eigenstates that exhibit squeezing in the momentum information entropy. Finally, we note that position information entropy increases with V 1 , but decreases with | V 2 |. However, the variation of momentum information entropy is contrary to that of the position information entropy.