Degeneracy of confined <i>D</i>‐dimensional harmonic oscillator

Montgomery, H. E.; Aquino, N.; Sen, K. D.

doi:10.1002/qua.21211

Cited by 47 publications

(58 citation statements)

References 35 publications

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“…On the other hand, setting¯ = µ = 1 = 1 2 and = = 0 gives the results of Ref. [38] for the results of exact harmonic oscillator energy states (cf. Eq.…”

Section: The Pseudoharmonic Potentialmentioning

confidence: 82%

On solutions of the Schrödinger equation for some molecular potentials: wave function ansatz

Ikhdair

Sever

2008

Open Physics

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Abstract:Making an ansatz to the wave function, the exact solutions of the D-dimensional radial Schrödinger equation with some molecular potentials, such as pseudoharmonic and modified Kratzer, are obtained. Restrictions on the parameters of the given potential, δ and η are also given, where η depends on a linear combination of the angular momentum quantum number and the spatial dimensions D and δ is a parameter in the ansatz to the wave function. On inserting D = 3, we find that the bound state eigensolutions recover their standard analytical forms in literature.

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“…On the other hand, setting¯ = µ = 1 = 1 2 and = = 0 gives the results of Ref. [38] for the results of exact harmonic oscillator energy states (cf. Eq.…”

Section: The Pseudoharmonic Potentialmentioning

confidence: 82%

On solutions of the Schrödinger equation for some molecular potentials: wave function ansatz

Ikhdair

Sever

2008

Open Physics

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“…We have employed the generalized pseudo-spectral (GPS) Legendre method with mapping, which is a fast algorithm that has been tested extensively and shown to yield the eigenvalues with an accuracy of twelve digits after the decimal. A more detailed account, with several applications of GPS, can be found in [30][31][32][33][34][35] and the references therein.…”

Section: Spectral Characteristicsmentioning

confidence: 99%

Spectral characteristics for a spherically confined −a/r+br²potential

Hall¹,

Saad²,

Sen³

2011

J. Phys. A: Math. Theor.

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We consider the analytical properties of the eigenspectrum generated by a class of central potentials given by V (r) = −a/r + br 2 , b > 0. In particular, scaling, monotonicity, and energy bounds are discussed. The potential V (r) is considered both in all space, and under the condition of spherical confinement inside an impenetrable spherical boundary of radius R. With the aid of the asymptotic iteration method, several exact analytic results are obtained which exhibit the parametric dependence of energy on a, b, and R, under certain constraints. More general spectral characteristics are identified by use of a combination of analytical properties and accurate numerical calculations of the energies, obtained by both the generalized pseudo-spectral method, and the asymptotic iteration method. The experimental significance of the results for both the free and confined potential V (r) cases are discussed.

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“…For a review on the topic, see e.g. 2–9 and the references therein. In most of the studies, however, only spherical confinement model is treated, though in some physical and chemical problems other boundary shapes are also of interest, e.g., cylindrical ones.…”

Section: Introductionmentioning

confidence: 99%

Shifts of the hydrogen atom in a cylindrical cavity

Yurenev

Scherbinin

Пупышев

2008

Int J of Quantum Chemistry

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ABSTRACT:Hydrogen atom in a cylindrical cavity is the simplest model for describing electronic states of the atom encapsulated into the nanotube. In the present work, simple analytical estimates for the electronic energy change under longitudinal and transversal shifts of the nucleus are made, using the first-order perturbation theory with the radius of the cavity as a perturbation parameter. Predicted signature of the electronic energy for the variety of atomic states agrees in essential details with the direct numerical estimations by finite difference and collocation procedures.

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Degeneracy of confined D‐dimensional harmonic oscillator

Cited by 47 publications

References 35 publications

On solutions of the Schrödinger equation for some molecular potentials: wave function ansatz

On solutions of the Schrödinger equation for some molecular potentials: wave function ansatz

Spectral characteristics for a spherically confined −a/r+br²potential

Shifts of the hydrogen atom in a cylindrical cavity

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Degeneracy of confined D‐dimensional harmonic oscillator

Cited by 47 publications

References 35 publications

On solutions of the Schrödinger equation for some molecular potentials: wave function ansatz

On solutions of the Schrödinger equation for some molecular potentials: wave function ansatz

Spectral characteristics for a spherically confined −a/r+br2potential

Shifts of the hydrogen atom in a cylindrical cavity

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Product

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Spectral characteristics for a spherically confined −a/r+br²potential