On the eigenvalues of the s-state radial equation of a spiked harmonic oscillator

Solano-Torres, W; Estévez, Gentil A.; Fernández, Francisco M.; Groenenboom, Gerrit C.

doi:10.1088/0305-4470/25/11/041

Cited by 25 publications

(16 citation statements)

References 31 publications

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“…The same restriction is shared by other studies of supersingular potentials (Aguilera-Navarro et al, 1990, 1992; Aguilera-Navarro and Guardiola, 1991; Aguilera-Navarro and Fern~-adez, 1991;Solano-Torres et al, 1992;Znojil, 1992). In order to have a better understanding of the effects of the presence of the supersingular components of the potential in such systems, it is necessary to investigate not only the ground state, but also the radially and rotationally excited states.…”

Section: Introductionmentioning

confidence: 78%

“…Since the papers by Klauder (1973), Ezawa et al (1975), and Detwiler and Klauder (1975) singular potentials have been receiving increased interest (Harrell, 1977;Klauder, 1978;de Llano, 1981;Znojil, 1982Znojil, , 1992Killingbeck, 1982;Ullah, 1986;Aguilera-Navarro et al, 1990, 1992AguileraNavarro and Guardiola, 1991;Fernfindez, 1991;Solano-Torres et al, 1992). These potentials are present in a number of situations which are mathematically challenging and physically interesting.…”

Section: Introductionmentioning

confidence: 99%

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Vibrational-rotational analysis of supersingular plus quadraticA/r 4+r 2 potential

Aguilera‐Navarro

Koo

1997

Int J Theor Phys

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Most work on supersingular potentials has focused on the study of the ground state. In this paper, a global analysis of the ground and excited states for the successive values of the orbital angular momentum of the supersingular plus quadratic potential is carried out, making use of centrifugal plus quadratic potential eigenfunction bases. First, the radially nodeless states are variationally analyzed for each value of the orbital angular momentum using the corresponding functions of the bases; the output includes the centrifugal and frequency parameters of the auxiliary potentials and their eigenfunction bases. In the second stage, these bases are used to construct the matrix representation of the Hamiltonian of the system, and from its diagonalization the energy eigenvalues and eigenvectors of the successive states are obtained. The systematics of the accuracy and convergence of the overall results are discussed with emphasis on the dependence on the intensity of the supersingular part of the potential and on the orbital angular momentum.

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Section: Introductionmentioning

confidence: 78%

Section: Introductionmentioning

confidence: 99%

Vibrational-rotational analysis of supersingular plus quadraticA/r 4+r 2 potential

Aguilera‐Navarro

Koo

1997

Int J Theor Phys

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“…This Hamiltonian has had a variety of applications in atomic, molecular, nuclear and particle physics, where it provides a simple model in which the potential has a repulsive core λx −α . Since the early investigations of Harrell, spiked harmonicoscillator potentials have become the subject of an intensive study lasting over two decades [3][4][5][6][7][8][9][10][11][12][13][14][15][16]. Most of this work is concerned with approximations for the energy of the problem in one spatial dimension, because the Klauder phenomenon [17][18][19] associated with the Hamiltonian (1.1) fails to occur in higher dimensions.…”

Section: Introductionmentioning

confidence: 99%

Generalized spiked harmonic oscillator

Hall

Saad

Keviczky

2001

J. Phys. A: Math. Gen.

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“…Also, in the region of α ≥ 5/2, it exhibits super-singularity. For many other facets of this potential, the reader is referred to the following references [20,[54][55][56][57][58][59][60][61][62], Both the α values considered can lead to super-singularity; these have been studied by numerous analytic, semi-analytic as well as numerical methodologies. Some of these literature results are given here for comparison.…”

Section: Resultsmentioning

confidence: 99%

“…Reference[55] b Reference[20] c Reference[54] d Reference[56] e Reference[57] f Reference[58] g Reference[59] h Reference[60] …”

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confidence: 99%

Ground and excited states of spherically symmetric potentials through an imaginary-time evolution method: application to spiked harmonic oscillators

Roy

2014

J Math Chem

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Starting from a time-dependent Schrödinger equation, stationary states of 3D central potentials are obtained. An imaginary-time evolution technique coupled with the minimization of energy expectation value, subject to the orthogonality constraint leads to ground and excited states. The desired diffusion equation is solved by means of a finite-difference approach to produce accurate wave functions, energies, probability densities and other expectation values. Applications in case of 3D isotropic harmonic oscillator, Morse as well the spiked harmonic oscillator are made. Comparison with literature data reveals that this is able to produce high-quality and competitive results. The method could be useful for this and other similar potentials of interest in quantum mechanics. Future and outlook of the method is briefly discussed.

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On the eigenvalues of the s-state radial equation of a spiked harmonic oscillator

Cited by 25 publications

References 31 publications

Vibrational-rotational analysis of supersingular plus quadraticA/r 4+r 2 potential

Vibrational-rotational analysis of supersingular plus quadraticA/r 4+r 2 potential

Generalized spiked harmonic oscillator

Ground and excited states of spherically symmetric potentials through an imaginary-time evolution method: application to spiked harmonic oscillators

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