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arXiv:quant-ph/0602203 · International Journal of Modern Physics B

QUANTUM INFORMATION ENTROPIES OF THE EIGENSTATES OF THE MORSE POTENTIAL

Ekrem Aydıner, Cenk Orta, R. Sever

Published Jan 30, 2008• 46 citations
arXivHTMLPDF

Abstract

The position and momentum space information entropies for the Morse potential are numerically obtained for different strengths of the potential. It is found to satisfy the bound obtained by Beckner, Bialynicki-Birula, and Mycielski. Interesting features of the entropy densities are graphically demonstrated.
DOI
10.1142/s021797920803848x

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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.
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The position and momentum space information entropies, of the ground state of the P\"oschl-Teller potential, are exactly evaluated and are found to satisfy the bound obtained by Beckner, Bialynicki-Birula, and Mycielski. These entropies for the first excited state, for different strengths of the potential well, are then numerically obtained. Interesting features of the entropy densities, owing their origin to the excited nature of the wave functions, are graphically demonstrated. We then compute the position space entropies of the coherent state of the P\"oschl-Teller potential, which is known to show revival and fractional revival. Time evolution of the coherent state reveals many interesting patterns in the space-time flow of information entropy.
Abstract In this work, the position and momentum space information densities of the Eckart potential are graphically demonstrated and their properties are studied. The position space information densities have quite an asymmetric shape depending on the values of quantum numbers. The information entropy is obtained and Bialynicki‐Birula and Mycielski inequality is numerically saturated for some parameters of the potential. It is shown that the inequality is saturated with increasing potential depth.