The H, H2+, and HeH2+ systems confined by an impenetrable spheroidal cavity: Revisited study via the <scp>L</scp>agrange‐mesh approach

Olivares-Pilón, Horacio; Cruz, S. A.

doi:10.1002/qua.25399

Cited by 12 publications

(10 citation statements)

References 46 publications

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“…The radial part of the wave function in such a spherical box can be written in terms of hypergeometric functions, the roots of which may then be calculated to obtain numerical values for the hydrogen energy spectrum [3,4,[19][20][21][22]. Although most effort has been focused on spherical boxes, there have been studies focused on other box geometries, including spheroids [23], cylinders [24], cubes [25,26] and certain polyhedra [27,28]. Others have studied the problem of off-centre hydrogen, where the nucleus is not located at the centre of the box [29,30]; the resulting asymmetry in the nucleus shifts the energy spectrum.…”

Section: Introductionmentioning

confidence: 99%

Compressed hydrogen atoms confined within generic boxes

Gorder

2022

Proc. R. Soc. A.

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The ‘compressed hydrogen atom’ problem involves solving the Schrödinger equation for a hydrogen atom confined within an impenetrable (often, spherical) box, with the wave function vanishing on the boundary of this box. To better understand the role the structure of the box plays on the compressed hydrogen atom, we study the compressed hydrogen atom in boxes of myriad shapes and sizes, developing a theory for how the structure of a generic box influences the hydrogen ground state energy. Our theory predicts that the ground state energy increases with the first Dirichlet eigenvalue (which encodes information on both the shape and size of a box) of the box and decreases with the distance of the nucleus from the boundary of the box. This theoretical prediction is supported by numerical simulations and variational approximations. Consideration is also given to the problem of a shell-confined hydrogen atom, with the electron confined to a separate ‘cage’ away from the nucleus. The behaviour of the shell-confined hydrogen ground state is well-approximated by a perturbation theory we develop for generic cages. Our results provide a unified framework for understanding confined, high-pressure hydrogen with relevance to applications ranging from crystal lattices of hydrogen to metallic hydrogen.

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Section: Introductionmentioning

confidence: 99%

Compressed hydrogen atoms confined within generic boxes

Gorder

2022

Proc. R. Soc. A.

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“…Many references among the vast literature on various physical aspects and applications of this topic can be found in Refs. [2,3,4]. To the best of my knowledge, Daniel Baye Physique Quantique and Physique Nucléaire Théorique et Physique Mathématique C.P.…”

Section: Introductionmentioning

confidence: 99%

Electromagnetic Transitions in the Spectrum of a Confined Hydrogen Atom

Baye

2022

Few-Body Syst

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Transition probabilities per time unit in the spectrum of the hydrogen atom conned in a spherical cavity are studied with the Dirac equation. The calculations are performed with simple and accurate expansions of the Dirac components provided by the Lagrange-mesh method with small numbers of scaled Jacobi mesh points. The initial and nal states as well as intermediate states occurring in two-photon transitions are described with a single Lagrange mesh. With this simplication, accurate matrix elements are easily computed with the Gauss quadrature associated with the Lagrange-Jacobi mesh. One-photon transitions are considered from the n = 2 and 3 levels. Most transition probabilities increase as a negative power of the connement radius when it becomes small. The two-photon 2s 1/2 − 1s 1/2 transition stops being the main deexcitation channel of the 2s 1/2 level when the connement radius decreases below about 15 atomic units. The 2p 1/2 and 2p 3/2 levels come below the 2s 1/2 level and allow a faster one-photon deexcitation.Keywords Conned hydrogen atom • Electromagnetic transition probabilities • Dirac equation • Lagrange-mesh method

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“…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%

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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The H, H₂⁺, and HeH²⁺ systems confined by an impenetrable spheroidal cavity: Revisited study via the Lagrange‐mesh approach

Cited by 12 publications

References 46 publications

Compressed hydrogen atoms confined within generic boxes

Compressed hydrogen atoms confined within generic boxes

Electromagnetic Transitions in the Spectrum of a Confined Hydrogen Atom

Confinement of hydrogen atom with Dirac equation

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The H, H2+, and HeH2+ systems confined by an impenetrable spheroidal cavity: Revisited study via the Lagrange‐mesh approach

Cited by 12 publications

References 46 publications

Compressed hydrogen atoms confined within generic boxes

Compressed hydrogen atoms confined within generic boxes

Electromagnetic Transitions in the Spectrum of a Confined Hydrogen Atom

Confinement of hydrogen atom with Dirac equation

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The H, H₂⁺, and HeH²⁺ systems confined by an impenetrable spheroidal cavity: Revisited study via the Lagrange‐mesh approach