Fisher information for the position-dependent mass Schrödinger system

Falaye, Babatunde J.; Serrano, F. A.; Dong, Shi‐Hai

doi:10.1016/j.physleta.2015.09.029

Cited by 80 publications

(55 citation statements)

References 21 publications

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“…The information theory of quantum‐mechanical systems is closely related to quantum communication and density functional methods . Therefore, intense theoretical studies on information‐theoretical measures for different quantum systems have been performed.…”

Section: Introductionmentioning

confidence: 99%

“…These studies are based on the different methods such as domain decomposition method, [18] energy conservative difference scheme, [19] conservative finite element method, [20] fractional Fan subequation method, [21] splitstep Fourier spectral method, [22] transfer-matrix method, [23] and so on.The information theory of quantum-mechanical systems is closely related to quantum communication and density functional methods. [24] Therefore, intense theoretical studies on information-theoretical measures for different quantum systems have been performed. In this way, different potential profiles in the Schrödinger equation have been assumed, for example, Dirac-delta-like potentials, [25] hyperbolical potential, [26] power-type This work is contributed to 80th Anniversary of Prof. Zhong-Qi Ma.…”

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confidence: 99%

“…The information theory of quantum-mechanical systems is closely related to quantum communication and density functional methods. [24] Therefore, intense theoretical studies on information-theoretical measures for different quantum systems have been performed. In this way, different potential profiles in the Schrödinger equation have been assumed, for example, Dirac-delta-like potentials, [25] hyperbolical potential, [26] power-type This work is contributed to 80th Anniversary of Prof. Zhong-Qi Ma.…”

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confidence: 99%

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Quantum information entropies of multiple quantum well systems in fractional Schrödinger equations

Solaimani

Dong

2019

Int J of Quantum Chemistry

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In this work, we study the position and momentum information entropies of multiple quantum well systems in fractional Schrödinger equations, which, to the best of our knowledge, have not so far been studied. Through a confining potential, their shape and number of wells (NOW) can be controlled by using a few tuning parameters; we present some interesting quantum effects that only appear in the fractional Schrödinger equation systems. One of the parameters denoted by the Ld can affect the position and momentum probability densities if the system is fractional (1 < α < 2). We find that the position (momentum) probability density tends to be more severely localized (delocalized) in more fractional systems (ie, in smaller values of α). Affecting the Ld on the position and momentum probability densities is a quantum effect that only appears in the fractional Schrödinger equations. Finally, we show that the Beckner Bialynicki‐Birula‐Mycieslki (BBM) inequality in the fractional Schrödinger equation is still satisfied by changing the confining potential amplitude Vconf, the NOW, the fractional parameter α, and the confining potential parameter Ld.

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Section: Introductionmentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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Quantum information entropies of multiple quantum well systems in fractional Schrödinger equations

Solaimani

Dong

2019

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%

“…[21] Other several investigations have been carried out for different quantum mechanical systems. [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36] We shall discuss in this work, the information-theoretic measures for the static screened Coulomb potential (SCP). This atomic model is essential because it is used in the nucleon-nucleon interaction arising from the pion-exchange mejachanism in nuclear physics.…”

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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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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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Fisher information for the position-dependent mass Schrödinger system

Cited by 80 publications

References 21 publications

Quantum information entropies of multiple quantum well systems in fractional Schrödinger equations

Quantum information entropies of multiple quantum well systems in fractional Schrödinger equations

Quantum information‐theoretic measures for the static screened Coulomb potential

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

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