Quantum information measures of infinite spherical well

Ye Jiao Shi, Guo Hua Sun, Farida Tahir, A. I. Ahmadov, Bing He, Shi Hai Dong

Research output: Contribution to journalArticlepeer-review

26 Scopus citations

Abstract

In this work, we study the Shannon information entropies Sr and Sp of an infinite spherical well. The Shannon entropy Sp is calculated numerically in terms of the analytical result of the wave function in momentum space. Some typical features of the position and momentum probability densities ρ(r) and ρ(p) as well as the information entropy densities ρs(r) and ρs(p) are demonstrated. We find that the position entropy Sr increases with the radius a of the spherical well for given quantum numbers l, m and n. It is interesting to note that the position entropy Sr decreases with the quantum numbers l and n for a fixed radius a and quantum number m. The position entropy Sr is almost independent of the quantum numbers l, m and n. The momentum entropy Sp first increases and then decreases with respect to the radius a. We also note that the Sr increases with the radius a and finally arrives at a constant. In addition, the Bialynicki-Birula-Mycielski (BBM) inequality is verified and also hold for this confined system.

Original languageEnglish
Article number1850088
JournalModern Physics Letters A
Volume33
Issue number16
DOIs
StatePublished - 30 May 2018

Keywords

  • BBM inequality
  • Shannon information entropy
  • infinitely spherical well

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