Entropic uncertainty measures for large dimensional hydrogenic systems

Puertas‐Centeno, David; Temme, Nico; Toranzo, I. V.; Dehesa, J. S.

doi:10.1063/1.5006569

Cited by 29 publications

(59 citation statements)

References 47 publications

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“…It is easily shown that in the neighborhood of α = 1/2 the left-hand side of Equation (31), which, as mentioned above, is valid accidentally for any state, behaves as…”

Section: Dirichlet Wellmentioning

confidence: 82%

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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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“…It is easily shown that in the neighborhood of α = 1/2 the left-hand side of Equation (31), which, as mentioned above, is valid accidentally for any state, behaves as…”

Section: Dirichlet Wellmentioning

confidence: 82%

“…Observe also that its left-hand side is a level-independent one. Figure 4 depicts dimensionless left-and right-hand sides of Equation (31), that is, the quantities…”

Section: Dirichlet Wellmentioning

confidence: 99%

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

Olendski

2020

Int J of Quantum Chemistry

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“…At first, the radial entropic moments x a r and x b p are calculated using wave functions in Equation 24 and definition in Equation 18, leading to following forms,…”

Section: Circular Statesmentioning

confidence: 99%

“…Extensive theoretical works have been published covering a broad variety of confining potentials. Two prototypical systems receiving maximum attention are harmonic oscillator (in 1D, 2D, 3D, D dimension) and confined hydrogen atom (CHA) inside a spherical enclosure . A CHA within an impenetrable (as well as penetrable) cavity was studied quite vigorously leading to a host of attractive properties—both from physical and mathematical point of view.…”

Section: Introductionmentioning

confidence: 99%

“…Two prototypical systems receiving maximum attention are harmonic oscillator (in 1D, 2D, 3D, D dimension) [9][10][11][12][13][14] and confined hydrogen atom (CHA) inside a spherical enclosure. [3,10,[15][16][17][18][19][20][21][22][23][24] A CHA within an impenetrable (as well as penetrable) cavity was studied quite vigorously leading to a host of attractive properties-both from physical and mathematical point of view. They offer many unique phenomena, especially relating to simultaneous, incidental and interdimensional degeneracy.…”

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confidence: 99%

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Information‐entropic measures in free and confined hydrogen atom

Mukherjee

Roy

2018

Int J of Quantum Chemistry

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Shannon entropy (S), Rényi entropy (R), Tsallis entropy (T), Fisher information (I), and Onicescu energy (E) have been explored extensively in both free H atom (FHA) and confined H atom (CHA). For a given quantum state, accurate results are presented by employing respective exact analytical wave functions in r space. The p‐space wave functions are generated from respective Fourier transforms—for FHA these can be expressed analytically in terms of Gegenbauer polynomials, whereas in CHA these are computed numerically. Exact mathematical expressions of Rrnormalα,Rpnormalβ, Trnormalα,Tpnormalβ,Er,Ep are derived for circular states of a FHA. Pilot calculations are done taking order of entropic moments (α, β) as (35,3) in r and p spaces. A detailed, systematic analysis is performed for both FHA and CHA with respect to state indices n, l, and with confinement radius (rc) for the latter. In a CHA, at small rc, kinetic energy increases, whereas Sboldr,Rboldrnormalα decrease with growth of n, signifying greater localization in high‐lying states. At moderate rc, there exists an interplay between two mutually opposing factors: (i) radial confinement (localization) and (ii) accumulation of radial nodes with growth of n (delocalization). Most of these results are reported here for the first time, revealing many new interesting features. Comparison with literature results, wherever possible, offers excellent agreement.

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Information‐Entropic Measures in Confined Isotropic Harmonic Oscillator

Mukherjee

Roy

2018

Advcd Theory and Sims

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Information based uncertainty measures like Rényi entropy (R), Shannon entropy (S) and Onicescu energy (E) (in both position and momentum space) are employed to understand the influence of radial confinement in isotropic harmonic oscillator. The transformation of Hamiltonian in to a dimensionless form gives an idea of the composite effect of oscillation frequency (ω) and confinement radius (r c ). For a given quantum state, accurate results are provided by applying respective exact analytical wave function in r space. The p-space wave functions are produced from Fourier transforms of radial functions. Pilot calculations are done taking order of entropic moments (α, β)as ( 3 5 , 3) in r and p spaces. A detailed, systematic analysis is performed for confined harmonic oscillator (CHO) with respect to state indices n r , l, and r c . It has been found that, CHO acts as a bridge between particle in a spherical box (PISB) and free isotropic harmonic oscillator (IHO). At smaller r c , E r increases and R α r , S r decrease with rise of n r . At moderate r c , there exists an interaction between two competing factors: (i) radial confinement (localization) and (ii) accumulation of radial nodes with growth of n r (delocalization). Most of these results are reported here for the first time, revealing many new interesting features.

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Entropic uncertainty measures for large dimensional hydrogenic systems

Cited by 29 publications

References 47 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

Information‐entropic measures in free and confined hydrogen atom

Information‐Entropic Measures in Confined Isotropic Harmonic Oscillator

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