Dimensionalities of weak solutions in hydrogenic systems

López‐Castillo, Alejandro; Oliveira, César R. de

doi:10.1088/0305-4470/39/13/020

Cited by 7 publications

(3 citation statements)

References 30 publications

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“…Spector and Lee [12] presented a relativistic treatment that removed the problem of infinite binding energy of the ground state. Several other works [13,14,15,16,17,18,19,20,21] (see also references therein) have discussed this apparently simple problem.…”

Section: Introductionmentioning

confidence: 99%

Self-adjoint extensions of Coulomb systems in 1, 2 and 3 dimensions

Oliveira

Verri

2009

Annals of Physics

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We study the nonrelativistic quantum Coulomb hamiltonian (i.e., inverse of distance potential) in R n , n = 1, 2, 3. We characterize their self-adjoint extensions and, in the unidimensional case, present a discussion of controversies in the literature, particularly the question of the permeability of the origin. Potentials given by fundamental solutions of Laplace equation are also briefly considered.

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Section: Introductionmentioning

confidence: 99%

Self-adjoint extensions of Coulomb systems in 1, 2 and 3 dimensions

Oliveira

Verri

2009

Annals of Physics

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“…Using non-usual separation of variables was possible to access different states. Based on that, we can infer the existence of other classes of state sets [9,10,13,22,25,33,42,[44][45][46][47][48][49][50]. However, it would be difficult to know what these sets of states and their size would be, using our current chemical knowledge.…”

Section: The Superlinear Convergence Of the Linear Combinations Of Slater And Gaussian Functionsmentioning

confidence: 99%

“…(f) theoretical description of atom and molecules at highly excited asymmetric states [57] for multi-electrons systems; (g) theoretical studies of the continuum [66] and resonance states [48,67], bound states in continuum [48,68], autoionizing systems [69], and their possible use of wavefunctions related to second rank Legendre functions [49].…”

Section: Generic Systemsmentioning

confidence: 99%

Searching for distinct classes of atomic and molecular states using convergence and separability criteria

López‐Castillo

2020

Theor Chem Acc

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We demonstrated that the solution ψ to the Schrodinger equation (SE) Ĥψ = εψ converges logarithmically in the classically forbidden region, i.e., as ε′ approaches to the correct eigenvalue ε, the approximate solution ψ′ logarithmically converges to ψ. Knowing that this approximate eigenvalue procedure generates a straightforward but inefficient method to solve a general problem of n-bodies, we thereby discuss the main characteristic of the usual methods to obtain a better convergence for atoms and molecules. Such usual methods consider that the solution of SE can be approached through a linear combination of solutions of systems with analytical solutions. Hydrogen-like atom solutions are used to describe atoms and molecules. This solution avoids the convergence problem of ψ′ even for approximate eigenvalues ε′ since all the terms of the linear combination decay asymptotically to zero. We argue that this type of solution works very well for a large class of almost separable atomic and molecular states in which the separation of electronic (and nucleus) movements occurs. We also establish a comparison of this separability and other systems, like gravitational, in which separability is only possible in particular classes of restricted systems. Finally, we consider the existence of distinct atomic and molecular states that may not be described using usual methods that apply this type of solution, which implies the separability of restricted problems. Therefore, usual methods to describe atoms and molecules may be insufficient to reach solutions with different or more general electronic correlations, as discussed in the text. Strategies to achieve general or distinctive solutions, although approximated, should be further studied and developed.

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Exact intrinsic half angular momentum from the Schrödinger equation

López‐Castillo

2020

Theor Chem Acc

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Dimensionalities of weak solutions in hydrogenic systems

Cited by 7 publications

References 30 publications

Self-adjoint extensions of Coulomb systems in 1, 2 and 3 dimensions

Self-adjoint extensions of Coulomb systems in 1, 2 and 3 dimensions

Searching for distinct classes of atomic and molecular states using convergence and separability criteria

Exact intrinsic half angular momentum from the Schrödinger equation

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