Position and momentum information-theoretic measures of a D-dimensional particle-in-a-box

López-Rosa, S.; Montero, Jesús; Sánchez-Moreno, P.; Venegas, José María Roa; Dehesa, J. S.

doi:10.1007/s10910-010-9790-3

Cited by 26 publications

(46 citation statements)

References 38 publications

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“…with ln(4π) = 2.5310…. This supplements an earlier conclusion of the independence of the momentum Rényi entropy on the quantum index at the large n. [37] For the continuous probability distributions, a dimensional incompatibility of the items entering the Tsallis entropies precludes their direct usage, but one can analyze the corresponding uncertainty relation from Equation (13), or, equivalently, Equation (11), which for our geometry reads F I G U R E 3 Sum of the position and momentum Rényi entropies R D ρ n α ð Þ+ R D γ n β ð Þ of the Dirichlet well as functions of the parameter α, where the solid line depicts the sum of the functionals of the ground orbital, the dashed curve is for the first excited state, the dotted one is for the level with n = 3, the dash-dotted dependence is for the state with n = 4, the upper (thick) dash-dot-dotted line is for n = 5, and its lower (thin) counterpart depicts function f(α) from Equation (27)…”

Section: Dirichlet Wellsupporting

confidence: 88%

“…Explanation of this phenomenon is the same as for the Rényi functionals. [37] Similar to them, the lowest energy quantity t D γ 1 is split off from its counterparts and, as the upper left inset demonstrates, tightens the entropic relation at α = 1/2. To explain this saturation, one has to point out that, at this value of the Tsallis factor, the left-hand side of Equation (11) for our geometry turns to…”

Section: Dirichlet Wellsupporting

confidence: 59%

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Rényi and Tsallis entropies of the Dirichlet and Neumann one‐dimensional quantum wells

Olendski

2020

Int J of Quantum Chemistry

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A comparative analysis of the Dirichlet and Neumann boundary conditions (BCs) of the one-dimensional (1D) quantum well extracts similarities and differences of the Rényi R(α) as well as Tsallis T(α) entropies between these two geometries. It is shown, in particular, that for either BC the dependences of the Rényi position components on the parameter α are the same for all orbitals but the lowest Neumann one, for which the corresponding functional R is not influenced by the variation of α. Lower limit α TH of the semi-infinite range of the dimensionless Rényi/Tsallis coefficient where momentum entropies exist crucially depends on the position BC and is equal to 1/4 for the Dirichlet requirement and 1/2 for the Neumann one. At α approaching this critical value, the corresponding momentum functionals do diverge. The gap between the thresholds α TH of the two BCs causes different behavior of the Rényi uncertainty relations as functions of α. For both configurations, the lowest energy level at α = 1/2 does saturate either type of the entropic inequality, thus confirming an earlier surmise about it. It is also conjectured that the threshold α TH of ½ is characteristic of any 1D non-Dirichlet system. Other properties are discussed and analyzed from the mathematical and physical points of view. K E Y W O R D S Dirichlet boundary condition, Neumann boundary condition, quantum well, Rényi entropy, Tsallis entropy

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Section: Dirichlet Wellsupporting

confidence: 88%

Section: Dirichlet Wellsupporting

confidence: 59%

Rényi and Tsallis entropies of the Dirichlet and Neumann one‐dimensional quantum wells

Olendski

2020

Int J of Quantum Chemistry

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“…They are widely used in quantum physics in the analysis of quantum entanglement, quantum revivals, atomic ionization properties . Other several investigations have been carried out for different quantum mechanical systems …”

Section: Introductionmentioning

confidence: 99%

Quantum information‐theoretic measures for the static screened Coulomb potential

Isonguyo

Oyewumi

Oyun

2018

Int J of Quantum Chemistry

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In this research work, the quantum information‐theoretic analysis of the static screened Coulomb potential has been carried out by studying both analytically and numerically the entropic measures, Fisher information as well as the Onicescu information energy of its wave function. Explicit expressions of these information‐theoretic measures were obtained. Using the Srivastava–Daoust linearization formula in terms of the multivariate Lauricella hypergeometric function, the Rényi entropy, Tsallis entropy, Onicescu information energy were analytically obtained. From the results obtained, it is observed that some of the Shannon entropies are negative, indicating that, negative entropies exists for the probability densities that are highly localized. The trends in the variation of the information‐theoretic measures with the potential screening parameter a for this atomic model are discussed. The Bialynicki‐Birula, Mycielski inequality (BBM), and the Fisher information based uncertainty relation are also verified.

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“…For γ = 0, equations (42) and (44) recover respectively the usual cases F [ρ n ] = π 2 n 2 a 2 and F [ ρ n ] = 4a 2 3 1 − 6 π 2 n 2 , according to [29]. Also, we have…”

Section: Complexities Analysis and Uncertainty Relationsmentioning

confidence: 69%

“…(35b) Figure 1 illustrates the energy eigenstates for the three states of the lowest energies with different values of γa, as well as their probability densities in the x and k spaces. For n = 10, we can see from the figure 2 that the average value of the quantum probability density (29) approaches to the classical probability density (30), in according to the correspondence principle. We also see that when γa increases the mass variation (in relation with the position) grows, which implies that the moment distribution turns out more localised around k = 0.…”

Section: Schrödinger Equation For Position-dependent Effective Mass Amentioning

confidence: 81%

Information-theoretic measures for a position-dependent mass system in an infinite potential well

Costa

Gomez

2020

Physica A: Statistical Mechanics and its Applications

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In this work we calculate the Cramér-Rao, the Fisher-Shannon and the López-Ruiz-Mancini-Calbert (LMC) complexity measures for eigenstates of a deformed Schrödinger equation, being this intrinsically linked with position-dependent mass (PDM) systems. The formalism presented is illustrated with a particle confined in an infinite potential well. Abrupt variation of the complexity near to the asymptotic value of the PDM-function m(x) and erasure of its asymmetry along with negative values of the entropy density in the position space, are reported as a consequence of the interplay between the deformation and the complexity.

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Position and momentum information-theoretic measures of a D-dimensional particle-in-a-box

Cited by 26 publications

References 38 publications

Rényi and Tsallis entropies of the Dirichlet and Neumann one‐dimensional quantum wells

Rényi and Tsallis entropies of the Dirichlet and Neumann one‐dimensional quantum wells

Quantum information‐theoretic measures for the static screened Coulomb potential

Information-theoretic measures for a position-dependent mass system in an infinite potential well

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