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Quantum uncertainties of the confined Harmonic Oscillator in position, momentum and phase‐space
Author(s) -
Laguna Humberto G.,
Sagar Robin P.
Publication year - 2014
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.201400156
Subject(s) - entropic uncertainty , position and momentum space , phase space , harmonic oscillator , physics , position (finance) , standard deviation , entropy (arrow of time) , quantum mechanics , uncertainty principle , momentum (technical analysis) , optical phase space , statistical physics , space (punctuation) , quantum , quantum harmonic oscillator , classical mechanics , mathematics , coherent states , squeezed coherent state , statistics , computer science , finance , economics , operating system
Quantum uncertainties in position, momentum and phase‐space are studied in the confined Harmonic Oscillator. Standard deviations and Shannon entropies are used to quantify these uncertainties and their behaviors are compared and contrasted. We observe a minimum in the momentum space Shannon entropy as the box length is increased, a feature that is not present in the momentum space standard deviation. The behaviors of the standard deviation product and the Shannon entropy sum, which form the basis of uncertainty relationships, are also analyzed. Maxima are observed in the product as the box length increases in sharp contrast to the entropy sum. The relationship between these behaviors and that of the Shannon entropy of the phase‐space Wigner function is analyzed and discussed. An analysis of the energetic components is also performed. The results reinforce the idea that the confined Harmonic Oscillator can be considered as an intermediate model which interpolates between the Particle in a Box Model and the Harmonic Oscillator and thus contains characteristics of both models.