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Chin. Phys. B, 2018, Vol. 27(4): 040301    DOI: 10.1088/1674-1056/27/4/040301
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Shannon information entropies for rectangular multiple quantum well systems with constant total lengths

M Solaimani1, Guo-Hua Sun(孙国华)2, Shi-Hai Dong(董世海)3
1. Department of Physics, Faculty of Science, Qom University of Technology, Qom, Iran;
2. Catedrática CONACyT, CIC, Instituto Politécnico Nacional, Unidad Profesional ALM, CDMX, C. P. 07700, Mexico;
3. Laboratorio de Información Cuántica, CIDETEC, Instituto Politécnico Nacional, Unidad Profesional ALM, CDMX, C. P. 07700, Mexico
Abstract  

We first study the Shannon information entropies of constant total length multiple quantum well systems and then explore the effects of the number of wells and confining potential depth on position and momentum information entropy density as well as the corresponding Shannon entropy. We find that for small full width at half maximum (FWHM) of the position entropy density, the FWHM of the momentum entropy density is large and vice versa. By increasing the confined potential depth, the FWHM of the position entropy density decreases while the FWHM of the momentum entropy density increases. By increasing the potential depth, the frequency of the position entropy density oscillation within the quantum barrier decreases while that of the position entropy density oscillation within the quantum well increases. By increasing the number of wells, the frequency of the position entropy density oscillation decreases inside the barriers while it increases inside the quantum well. As an example, we might localize the ground state as well as the position entropy densities of the 1st, 2nd, and 6th excited states for a four-well quantum system. Also, we verify the Bialynicki-Birula-Mycieslki (BBM) inequality.

Keywords:  position and momentum Shannon entropies      multiple quantum well      entropy densities  
Received:  26 October 2017      Revised:  22 December 2017      Published:  05 April 2018
PACS:  03.65.-w (Quantum mechanics)  
  03.65.Ge (Solutions of wave equations: bound states)  
  03.67.-a (Quantum information)  
Fund: 

Project supported by the Iranian Nanotechnology Initiative Council (INIC), the 20180677-SIP-IPN, Mexico, and the CONACYT 288856-CB-2016, Mexico.

Corresponding Authors:  M Solaimani, Shi-Hai Dong     E-mail:  solaimani.mehdi@gmail.com,solaimani@qut.ac.ir;dongsh2@yahoo.com

Cite this article: 

M Solaimani, Guo-Hua Sun(孙国华), Shi-Hai Dong(董世海) Shannon information entropies for rectangular multiple quantum well systems with constant total lengths 2018 Chin. Phys. B 27 040301

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