Phase-Space Position-Momentum Correlation and Potentials

Laguna, Humberto G.; Sagar, Robin P.

doi:10.3390/e15051516

Cited by 9 publications

(11 citation statements)

References 33 publications

(37 reference statements)

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“…The simplest system, the particle in a box, is used in textbooks to introduce fundamental concepts such as the quantization of energy. There are studies on the behavior of confined systems with different potentials . Some models are studied in connection with the effect of “pressure” on quantum systems.…”

Section: Introductionmentioning

confidence: 99%

Quantum uncertainties of the confined Harmonic Oscillator in position, momentum and phase‐space

Laguna

Sagar

2014

Annalen der Physik

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Quantum uncertainties in position, momentum and phasespace 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.

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Section: Introductionmentioning

confidence: 99%

Quantum uncertainties of the confined Harmonic Oscillator in position, momentum and phase‐space

Laguna

Sagar

2014

Annalen der Physik

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“…The entropy sum has been proposed as a measure of basis set quality in quantum chemical calculations, as a correlation measure in atomic systems, and as a measure of the localization‐delocalization in a separable phase‐space distribution . As such, it is one measure of the position‐momentum correlation . It has been studied in a variety of models, fermionic and bosonic systems including Bose‐Einstein condensates .…”

Section: Introductionmentioning

confidence: 99%

Shannon‐information entropy sum in the confined hydrogenic atom

Salazar

Laguna

Prasad

et al. 2020

Int J of Quantum Chemistry

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The appearance of critical points in the Shannon entropy sum as a function of confinement radius, in ground and excited state confined hydrogenic systems, is discussed. We illustrate that the Coulomb potential in tandem with the hard sphere confinement are responsible for these points. The positions of these points are observed to vary with the intensity of the potential. The effects of the Coulomb potential on the system are further probed, by examining the differences between the densities of the confined atom and those of the particle confined in a spherical box, for the same confinement radius. These differences are quantified by using Kullback-Leibler and cumulative residual Kullback-Leibler distance measures from information theory. These measures detect that the effects of the Coulomb potential are squeezed out of the system as the confinement radius decreases. That is, the confined atom densities resemble the particle in a box ones, for smaller confinement radii. Furthermore, the critical points in the entropy sum lie in the same regions where there are changes in the distance measures, as the atom behaves more particle in a spherical box-like. The analysis is further complemented by examination of the derivative of the entropy sum with respect to confinement radius. This study illustrates the inhomogeneity in the magnitudes of the derivatives of the entropy sum components and their dependence on the Coulomb potential. A link between the derivative and the entropic force is also illustrated and discussed. Similar behaviors are observed when the virial ratio is compared to the entropic power one, as a function of confinement radius. K E Y W O R D S confined hydrogen atom, Kullback-Leibler distance measures, quantum uncertainties, Shannon entropy sum

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“…where the quantum numbers ( ) On the other hand, to derive the wave function in momentum space, we can apply the Fourier transform to Equation (8). However, a simpler way to derive such wave function is to rewrite the Hamiltonian in momentum coordinates, which is given by:…”

Section: Moshinsky Modelmentioning

confidence: 99%

“…Using different phase-spaces to measure Shannon entropy will lead to different expressions. Studies of Shannon entropy in position space and momentum space of atomic systems have been carried out [7][8][9][10][11][12][13][14]. We calculate Shannon entropy in position basis and momentum basis to discuss the correlation.…”

Section: Open Accessmentioning

confidence: 99%

Statistical Correlations of the N-particle Moshinsky Model

Peng

2015

Entropy

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Abstract:We study the correlation of the ground state of an N-particle Moshinsky model by computing the Shannon entropy in both position and momentum spaces. We have derived the Shannon entropy and mutual information with analytical forms of such an N-particle Moshinsky model, and this helps us test the entropic uncertainty principle. The Shannon entropy in position space decreases as interaction strength increases. However, Shannon entropy in momentum space has the opposite trend. Shannon entropy of the whole system satisfies the equality of entropic uncertainty principle. Our results also indicate that, independent of the sizes of the two subsystems, the mutual information increases monotonically as the interaction strength increases.

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Phase-Space Position-Momentum Correlation and Potentials

Cited by 9 publications

References 33 publications

Quantum uncertainties of the confined Harmonic Oscillator in position, momentum and phase‐space

Quantum uncertainties of the confined Harmonic Oscillator in position, momentum and phase‐space

Shannon‐information entropy sum in the confined hydrogenic atom

Statistical Correlations of the N-particle Moshinsky Model

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