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Physica Scripta

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

Guo-Hua Sun, Shi‐Hai Dong

Published Feb 28, 2013• 71 citations
Publisher

Abstract

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.

DOI
10.1088/0031-8949/87/04/045003

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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.
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.
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.
Abstract In this article, some information theoretic concepts are analyzed for modified Hylleraas plus exponential Rosen Morse potential in position and momentum space. The angular and radial contributions of the information density are graphically demonstrated for different states. The entropy densities have asymmetric shape which depends on the values of quantum numbers. The information entropy is analytically obtained for ground state of the potential whereas the numerical calculations have been performed for the higher states and Bialynicki‐Birula and Mycielski inequality is tested for various states using different parameters of the potential. It is shown that the information entropy is reduced, both in position and momentum space, for careful selection of some parameters. Further, it is found that there exist eigenstates exhibiting squeezing in information entropy of modified Hylleraas plus exponential Rosen Morse and Eckart potential. Interestingly, in case of Eckart potential, the squeezed states are obtained in position as well as momentum space and are attempted to saturate for some values of the parameters.