A Particle Interacting with V-shaped Potential Decorated by a Dirac Delta Function Interaction at Center

Wang, Xin; Liang-Hui, Tang; Reng-Lai, Wu; Wang, Nan; Liu, Quanhui

doi:10.1088/0253-6102/53/2/08

Cited by 5 publications

(4 citation statements)

References 13 publications

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“…As shown in Ref. [25], the ground state energy eigenvalue decreases without a lower limit as σ increases (attractive case). However, the energies of the excited even states are limited by the energies E 2n+1 of odd states and as σ → ∞, E 2n+2 → E 2n+1 where n = 0, 1, .…”

Section: Ai Functionmentioning

confidence: 59%

“…The Schrödinger for a particle in the V-shaped potential decorated by a repulsive or attractive Dirac delta function interaction at the center has been solved very recently. [25] We apply this potential as a model for quadrupole trap with a dimple. We also compare the results of this paper with the results of a previous paper in which the harmonic trap with a dimple potential in 1D was investigated.…”

Section: Introductionmentioning

confidence: 99%

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Bose—Einstein Condensate in a Linear Trap with a Dimple Potential

Uncu

Tarhan

2013

Commun. Theor. Phys.

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We study Bose-Einstein condensation in a linear trap with a dimple potential where we model dimple potentials by Dirac δ function. Attractive and repulsive dimple potentials are taken into account. This model allows simple, explicit numerical and analytical investigations of noninteracting gases. Thus, the Schrödinger equation is used instead of the Gross-Pitaevski equation. We calculate the atomic density, the chemical potential, the critical temperature and the condensate fraction. The role of the relative depth of the dimple potential with respect to the linear trap in large condensate formation at enhanced temperatures is clearly revealed. Moreover, we also present a semi-classical method for calculating various quantities such as entropy analytically. Moreover, we compare the results of this paper with the results of a previous paper in which the harmonic trap with a dimple potential in 1D was investigated.

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Section: Ai Functionmentioning

confidence: 59%

Section: Introductionmentioning

confidence: 99%

Bose—Einstein Condensate in a Linear Trap with a Dimple Potential

Uncu

Tarhan

2013

Commun. Theor. Phys.

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“…This problem was considered in the past [23], but only for q = 0. In the present case case, the Lippman-Schwinger equation (4.2) is…”

Section: Absolute Value Potential With Additional δ Interactionmentioning

confidence: 99%

“…Let us analyze now the effect of the presence of a δ perturbation V a (x, q) = a δ(x − q), a ∈ R, on the eigenstates of the absolute value potential. This problem was considered in the past [23], but only for q = 0. In the present case case, the Lippman-Schwinger equation (4.2) is…”

Section: Absolute Value Potential With Additional δ Interactionmentioning

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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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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A Particle Interacting with V-shaped Potential Decorated by a Dirac Delta Function Interaction at Center

Cited by 5 publications

References 13 publications

Bose—Einstein Condensate in a Linear Trap with a Dimple Potential

Bose—Einstein Condensate in a Linear Trap with a Dimple Potential

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

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