Fine structure in the hydrogen atom boxed in a spherical impenetrable cavity

Rojas, R.; Aquino, N.; Flores-Riveros, A.

doi:10.1002/qua.25584

Cited by 10 publications

(15 citation statements)

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“…(3.72), (3.77) and (3.79), respectively, for R = [1,6], reported previously by the authors, compared with those of high accuracy from its Refs. [29] and [39].…”

Section: 11mentioning

confidence: 99%

Recent progress in confined atoms and molecules: Superintegrability and symmetry breakings

Koo

2018

Rev. Mex. Fís.

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This review article has the antecedents of Jaskolski’s 1996 Physics Report Confined Many-electron Systems , the fifteen chapters on the Theory of Confined Quantum Systems in Vols. 57 and 58 of 2009 Advances in Quantum Chemistry, and the nine chapters of the 2014 Monograph “Electronic Structure of Confined Quantum Atoms and Molecules”. In this contribution the last two sets of reviews are taken as the points of reference to illustrate some advances in several lines of research in the elapsed periods. The recent progress is illustrated on the basis of a selection of references from the literature taking into account the confined quantum systems, the confining environments and their modelings; their properties and processes, emphasizing the changes due to the confinement; the methods of analysis and solutions, their results including confiability and accuracy; as well as applications in other areas. The updated and current works of the Reviewer are also presented. The complementary words in the title apply to the simplest atom in its free configuration and to the harmonic oscillator quantum dot because they admit more exact solutions than the number of their degrees of freedom; and to their many-electron and confined counterparts, due to their additional interactions and changes in boundary conditions.

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“…(3.72), (3.77) and (3.79), respectively, for R = [1,6], reported previously by the authors, compared with those of high accuracy from its Refs. [29] and [39].…”

Section: 11mentioning

confidence: 99%

Recent progress in confined atoms and molecules: Superintegrability and symmetry breakings

Koo

2018

Rev. Mex. Fís.

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“…For the Coulomb potential, the three terms are calculated with equations (18)-(20) of ref. [5] where the matrix elements…”

Section: A P P E N D I X B : Pauli Approximationmentioning

confidence: 99%

“…Many references among the vast literature on various physical aspects and applications of this topic can be found in refs. [2][3][4][5].…”

Section: Introductionmentioning

confidence: 99%

“…Many references among the vast literature on various physical aspects and applications of this topic can be found in refs. [2][3][4][5].In the spherical case, a hard confinement is obtained by limiting the configuration space at some radius while a soft confinement makes use of an additional potential damping the wave function at large distances. A hydrogen atom confined in an impenetrable spherical cavity of radius R has been much studied nonrelativistically with the Schrödinger equation.…”

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confidence: 99%

“…They allow a precise comparison with the fine-structure corrections in the Pauli approximation, which have been recently computed for the hydrogen atom. [5,13] The Lagrange-mesh method is an approximate variational calculation using a special basis of N functions, called Lagrange functions, related to a set of N mesh points and the Gauss quadrature associated with this mesh. [14][15][16][17] The Lagrange functions are infinitely differentiable and vanish at all points of the mesh, except one.…”

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confidence: 99%

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Confinement of hydrogen atom with Dirac equation

Baye

2019

Int J of Quantum Chemistry

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The problem of a particle confined in a spherical cavity is studied with the Dirac equation. A hard confinement is obtained by forcing the large component to vanish at the cavity radius. It is shown that the small component cannot vanish simultaneously at this radius. In the case of a confined hydrogen atom, the energies are given by an implicit equation. For some values of the radius, explicit analytical expressions of the energy exist like in the nonrelativistic case. Very accurate energies and wave functions are obtained with the Lagrange‐mesh method with few mesh points. To this end, two differently regularized Lagrange‐Jacobi bases associated with the same mesh are used for the large and small components. The importance of relativistic effects is discussed for hydrogen‐like ions. The validity of this definition of hard confinement is discussed with a soft‐confinement model studied with the R‐matrix method.

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Two‐dimensional confined hydrogen: An entropy and complexity approach

Estañón

Aquino

Puertas‐Centeno

et al. 2020

Int J of Quantum Chemistry

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The position and momentum spreading of the electron distribution of the two-dimensional confined hydrogenic atom, which is a basic prototype of the general multidimensional confined quantum systems, is numerically studied in terms of the confinement radius for the 1s, 2s, 2p, and 3d quantum states by means of the main entropy and complexity information-theoretical measures. First, the Shannon entropy and the Fisher information, as well as the associated uncertainty relations, are computed and discussed. Then, the Fisher-Shannon, lopezruiz-mancini-alvet, and LMC-Rényi complexity measures are examined and mutually compared. We have found that these entropy and complexity quantities reflect the rich properties of the electron confinement extent in the two conjugated spaces. K E Y W O R D SFisher information of the two-dimensional confined hydrogen atom, Fisher-Shannon complexity measure of the two-dimensional confined hydrogen atom, LMC-Rényi complexity measure of the two-dimensional confined hydrogen atom, Shannon entropy of the two-dimensional confined hydrogen atom, two-dimensional confined hydrogen atom | INTRODUCTIONThe fundamental and practical relevance of the spherically confined quantum systems has been manifested from the early days of quantum physics [1,2] up until now. [3][4][5][6][7] They have been used as prototypes to explain numerous phenomena and systems not only in the three-dimensional world but also for nonrelativistic and relativistic D-dimensional (D ≥ 2) chemistry and physics. [8][9][10][11][12][13][14] For example, pioneered by Gerhard Ertl, the 2007 Nobel Laureate in Chemistry, and his collaborators, surface chemistry has been extensively studied and has become a key branch in chemistry. [11][12][13] In physics of materials, two-dimensional systems have been used to gain insight into the properties of semiconductors (see, eg, refs. [15, 16]), and they start to play a fundamental role in bringing strong and new forms of control to the atomic-scale limit over the dynamics of matter in the extreme confinement of electromagnetic energy by phonon polaritonics. [10] Moreover, the properties of the real fluids can be studied by means of crystalline fluids (ie, with a symmetry) with nonstandard dimensions (see, eg, ref. [17]).The idea of two-and multidimensional spherical confinement of atoms has been used not only to simulate the effect of high pressure on the static dipole polarizability in hydrogen [18] but also to model a great deal of nanotechnological objects such as quantum dots; quantum wells and quantum wires; [19,20] atoms and molecules embedded in nanocavities, for example, in fullerenes, zeolites cages, and helium droplets; [4,6,7,[21][22][23] dilute bosonic and fermionic systems in magnetic traps of extremely low temperatures; [24][25][26] and a variety of quantum-information elements. [27,28] This has provoked a fast development of a density functional theory of independent particles moving in multidimensional central potentials with various analytical forms (see, eg, refs. [5-7, 29-...

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Fine structure in the hydrogen atom boxed in a spherical impenetrable cavity

Cited by 10 publications

References 49 publications

Recent progress in confined atoms and molecules: Superintegrability and symmetry breakings

Recent progress in confined atoms and molecules: Superintegrability and symmetry breakings

Confinement of hydrogen atom with Dirac equation

Two‐dimensional confined hydrogen: An entropy and complexity approach

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