Bound states and scattering coefficients of the potential

Gadella, M.; Negro, J.; Nieto, L. M.

doi:10.1016/j.physleta.2009.02.025

Cited by 89 publications

(176 citation statements)

References 14 publications

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“…This work also serves as an exploratory study of models and techniques which we hope to apply to a new class of inhomogeneous quantum wells. Another natural step is to study stronger singular perturbations such as the Dirac delta derivatives considered in [8,24,25,26]. This analysis requires a more careful study and is work in progress.…”

Section: Summary and Discussionmentioning

confidence: 99%

The energy level structure of a variety of one-dimensional confining potentials and the effects of a local singular perturbation

Glasser

Nieto

2015

Can. J. Phys.

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Motivated by current interest in quantum confinement potentials, especially with respect to the Stark spectroscopy of new types of quantum wells, we examine several novel one-dimensional singular oscillators. A Green function method is applied, the construction of the necessary resolvents is reviewed and several new ones are introduced. In addition, previous work on the singular harmonic oscillator model, introduced by Avakian et al. is reproduced to verify the method and results. A novel features is the determination of the spectra of asymmetric hybrid linear and quadratic potentials. As in previous work, the singular perturbations are modeled by delta functions.

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Section: Summary and Discussionmentioning

confidence: 99%

The energy level structure of a variety of one-dimensional confining potentials and the effects of a local singular perturbation

Glasser

Nieto

2015

Can. J. Phys.

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“…A second δ ′ interaction, which is compatible with the δ interaction, so that we may compose interactions of the form [65][66][67], comes from the consideration of the following matching conditions for the wave function at the origin:…”

Section: Introductionmentioning

confidence: 99%

Spectroscopy of a one-dimensional V-shaped quantum well with a point impurity

et al. 2018

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a b s t r a c tWe consider the one-dimensional Hamiltonian with a V-shaped, decorated with a point impurity of either δ-type, or local δ ′ -type or even nonlocal δ ′ -type, thus yielding three exactly solvable models. We analyse the behaviour of the change in the energy levels when an interaction of the type −λ δ(x) or −λ δ(x − x 0 ) is switched on. In the first case, even energy levels, pertaining to antisymmetric bound states, remain invariant with respect to λ even though odd energy levels, pertaining to symmetric bound states, decrease as λ increases. In the second, all energy levels decrease when the factor λ increases. A similar study has been performed for the so-called nonlocal δ ′ interaction, requiring a coupling constant renormalisation, which implies the replacement of the form factor λ by a renormalised form factor β. In terms of β, odd energy levels are unchanged. However, we show the existence of level crossings: after a fixed value of β the energy of each even level, with the natural exception of the first one, becomes lower than the constant energy of the previous odd level. Finally, we consider an interaction of the type −λδ(x)+µδ ′ (x), and analyse in detail the discrete spectrum of the resulting selfadjoint Hamiltonian.

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“…Finally, in a series of three papers [7][8][9], light propagation in a one-dimensional realistic dielectric superlattice, modeled by means of a periodic array of Dirac delta functions, is investigated for the cases of transverse electric, transverse magnetic, and omnidirectional polarization modes. Nevertheless, examples of the use of potentials related to the derivative of the Dirac delta function δ (x) have appeared in the literature only very recently [10], and in a rather abstract context. Indeed, this may be due, in part, to the fact that there has been some controversy on the meaning of the δ (x) potential [11][12][13][14], since different regularizations produce different reflection and transmission coefficients.…”

Section: Introductionmentioning

confidence: 99%

One Dimensional Models with a Singular Potential of the Type −αδ(x)+βδ′(x)

2010

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We study a one-dimensional singular potential plus two types of regular interactions: constant electric field and harmonic oscillator. In order to search for the bound state energies, we shall use the Lippman-Schwinger Green function technique. Another direct method will be mentioned for the harmonic oscillator. In the electric field case the unique bound state coincides with that found in an earlier study as the field is switched off. For non-zero field the ground state is shifted and positive energy "quasibound states" appear. The harmonic oscillator demonstrates the general result that for a symmetric potential the odd states are not altered whereas the even states energies are lowered or raised accordingly as the delta perturbation is attractive or repulsive. No states are created or annihilated.

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Bound states and scattering coefficients of the potential

Cited by 89 publications

References 14 publications

The energy level structure of a variety of one-dimensional confining potentials and the effects of a local singular perturbation

The energy level structure of a variety of one-dimensional confining potentials and the effects of a local singular perturbation

Spectroscopy of a one-dimensional V-shaped quantum well with a point impurity

One Dimensional Models with a Singular Potential of the Type −αδ(x)+βδ′(x)

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