Information-theoretic measures for Morse and Pöschl–Teller potentials

Dehesa, J. S.; Martínez–Finkelshtein, Andrei; Сорокин, В. Н.

doi:10.1080/00268970500493243

Cited by 113 publications

(101 citation statements)

References 18 publications

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“…Contrary to the quantum entropies, which always obey the lower bound from Eq. (16), similar universal relation between position and momentum components of the Fisher information is not known though for several particular systems some inequalities have been derived [52][53][54][55][56]. In quantum mechanics, one of its main applications is due to the fact that it enters into the expression for the kinetic energy of the manyparticle system [57] and in this way establishes the link between, for example, density functional methods and information theory.…”

Section: Introductionmentioning

confidence: 99%

Theory of the Robin quantum wall in a linear potential. I. Energy spectrum, polarization and quantum‐information measures

Olendski

2016

Annalen der Physik

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Information-theoretical concepts are employed for the analysis of the interplay between a transverse electric field E applied to a one-dimensional surface and Robin boundary condition (BC), which with the help of the extrapolation length Λ zeroes at the interface a linear combination of the quantum mechanical wave function and its spatial derivative, and its influence on the properties of the structure. For doing this, exact analytical solutions of the corresponding Schrödinger equation are derived and used for calculating energies, dipole moments, position Sx and momentum S k quantum information entropies and their Fisher information Ix and I k and Onicescu information energies Ox and O k counterparts. It is shown that the weak (strong) electric field changes the Robin wall into the Dirichlet, Λ = 0 (Neumann, Λ = ∞), surface. This transformation of the energy spectrum and associated waveforms in the growing field defines an evolution of the quantum-information measures; for example, it is proved that for the Dirichlet and Neumann BCs the position (momentum) quantum information entropy varies as a positive (negative) natural logarithm of the electric intensity what results in their field-independent sum Sx + S k . Analogously, at Λ = 0 and Λ = ∞ the position and momentum Fisher informations (Onicescu energies) depend on the applied voltage as E 2/3 (E 1/3 ) and its inverse, respectively, leading to the field-independent product IxI k (OxO k ). Peculiarities of their transformations at the finite nonzero Λ are discussed and similarities and differences between the three quantum-information measures in the electric field are highlighted with the special attention being paid to the configuration with the negative extrapolation length.

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Section: Introductionmentioning

confidence: 99%

Theory of the Robin quantum wall in a linear potential. I. Energy spectrum, polarization and quantum‐information measures

Olendski

2016

Annalen der Physik

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“…This line of inquiry has recently led to numerous researchers to calculate the measures of information for various quantummechanical potentials of a specific analytic form [1][2][3][4][5][6][7][8][9] as well as for hydrogenic systems with standard and nonstandard dimensionalities [3,8,[10][11][12][13], circular membranes [14], confined systems [15,16], and many-electron systems [17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Entropic functionals of Laguerre polynomials and complexity properties of the half‐line Coulomb potential

Sánchez-Moreno

Omiste

Dehesa

2011

Int J of Quantum Chemistry

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ABSTRACT:The stationary states of the half-line Coulomb potential are described by quantum-mechanical wavefunctions, which are controlled by the Laguerre polynomials L (1) n (x). Here, we first calculate the qth-order frequency or entropic moments of this quantum system, which is controlled by some entropic functionals of the Laguerre polynomials. These functionals are shown to be equal to a Lauricella function F, 1) by use of the Srivastava-Niukkanen linearization relation of Laguerre polynomials. The resulting general expressions are applied to obtain the following information-theoretic quantities of the half-line Coulomb potential: disequilibrium, Renyi and Tsallis entropies. An alternative and simpler expression for the linear entropy is also found by means of a different method. Then, the Shannon entropy and the LMC shape complexity of the lowest and highest (Rydberg) energetic states are explicitly given; moreover, sharp information-theoretic-based upper bounds to these quantities are found for general physical states. These quantities are numerically discussed for the ground and various excited states. Finally, the uncertainty measures of the half-line Coulomb potential given by the information-theoretic lengths are discussed.

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“…The disorder aspect has been discussed in depth by Frieden [23,24], and the uncertainty properties are clearly shown by the Stam inequalities [52] and the recently discovered Fisher-information-based uncertainty relation [7,14] I(ρ)I(ρ) ≥ 4, whereρ denotes the probability density associated to the Fourier transform of the variable X. For a deeper understanding of the Fisher notion, let us point out that broad and smooth densities have low gradient contents and so their Fisher information is small.…”

Section: The Fisher Informationmentioning

confidence: 99%

“…As already pointed out, these functions satisfy Eqs. (3) or (13) and (14). The relative Fisher information of these functions with respect to the Pearson weight function ω(x) given by Eq.…”

Section: Relative Fisher Information Of Special Functionsmentioning

confidence: 99%

Fisher information of special functions and second-order differential equations

Yáñez

Sánchez-Moreno

Zarzo

et al. 2008

Journal of Mathematical Physics

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We investigate a basic question of information theory, namely the evaluation of the Fisher information and the relative Fisher information with respect to a nonnegative function, for the probability distributions obtained by squaring the special functions of mathematical physics which are solutions of second-order differential equations. Emphasis is made in the Nikiforov-Uvarov hypergeometric-type functions. We obtain explicit expressions for these information-theoretic properties via the expectation values of the coefficients of the differential equation. We illustrate our approach for various special functions of physico-mathematical interest.

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Information-theoretic measures for Morse and Pöschl–Teller potentials

Cited by 113 publications

References 18 publications

Theory of the Robin quantum wall in a linear potential. I. Energy spectrum, polarization and quantum‐information measures

Theory of the Robin quantum wall in a linear potential. I. Energy spectrum, polarization and quantum‐information measures

Entropic functionals of Laguerre polynomials and complexity properties of the half‐line Coulomb potential

Fisher information of special functions and second-order differential equations

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