Open AccessSTUDY OF SHANNON ENTROPY IN THE CONTEXT OF QUANTUM MECHANICS: AN APPLICATION TO FREE AND CONFINED HARMONIC OSCILLATOR
Author(s) -
Wallas S. Nascimento,
Frederico V. Prudente
Publication year - 2016
Publication title -
química nova
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.214
H-Index - 73
eISSN - 1678-7064
pISSN - 0100-4042
DOI - 10.5935/0100-4042.20160045
Subject(s) - harmonic oscillator , entropic uncertainty , joint quantum entropy , mathematics , entropy (arrow of time) , rényi entropy , quantum mechanics , statistical physics , shannon's source coding theorem , physics , information theory , quantum , maximum entropy thermodynamics , principle of maximum entropy , uncertainty principle , statistics
The aim of this study was a didactic presentation of the Shannon entropy in the quantum theory context, followed by application to the case of a one-dimensional harmonic oscillator in its ground state, both in the free case and confined case. The study of these systems allows us to highlight notions such as location or delocation of a particle, a possible interpretation that the Shannon entropy can adopt. The Shannon entropy in position (Sx) and momentum (Sp) spaces were calculated for both systems, beyond the entropic sum (St = Sx + Sp). With this procedure it was possible to identify trends in the behavior of the Shannon entropy (Sx and Sp) and test the compliance of the entropic uncertainty relation (St = Sx + Sp ≥ n(1 + ln(π)))