Mass-jump and mass-bump boundary conditions for singular self-adjoint extensions of the Schrödinger operator in one dimension

Kulinskii, V. L.; Panchenko, Dmitry

doi:10.1016/j.aop.2019.03.001

Cited by 11 publications

(14 citation statements)

References 28 publications

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“…This approach has been used to construct several one-dimensional models which go beyond the Dirac delta potential [14,15]. A discussion on the physical meaning of the one-dimensional contact potentials constructed as self-adjoint extensions of the kinetic energy operator is given in [16,17]. It is remarkable that, inspired in the physics of contact interactions, new mathematics has been developed [18].…”

Section: Introductionmentioning

confidence: 99%

An approximation to the Woods–Saxon potential based on a contact interaction

et al. 2020

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We study a non-relativistic particle subject to a three-dimensional spherical potential consisting of a finite well and a radial δ − δ contact interaction at the well edge. This contact potential is defined by appropriate matching conditions for the radial functions, thereby fixing a self-adjoint extension of the non-singular Hamiltonian. Since this model admits exact solutions for the wave function, we are able to characterize and calculate the number of bound states. We also extend some well-known properties of certain spherically symmetric potentials and describe the resonances, defined as unstable quantum states. Based on the Woods-Saxon potential, this configuration is implemented as a first approximation for a mean-field nuclear model. The results derived are tested with experimental and numerical data in the double magic nuclei 132 Sn and 208 Pb with an extra neutron.

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Section: Introductionmentioning

confidence: 99%

An approximation to the Woods–Saxon potential based on a contact interaction

et al. 2020

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“…Due to their wide range of physical applications contact potentials in quantum physics have been a very active research field recently. After the seminal paper by Kurasov where contact potentials are characterised by certain self adjoint extensions of the one-dimensional kinetic operator K = −d 2 /dx 2 [21], several attempts have been made to explain the physical meaning of the contact potentials that emerge from these extensions [22,23]. More recently there have been papers where, contact potentials have been used to study the effects of resonant tunneling [24,25], to study their properties under the effect of external fields [26], and their applications in the study of metamaterials [27].…”

Section: Introductionmentioning

confidence: 99%

Band spectra of periodic hybrid $δ$-$δ^\prime$ structures

Gadella,

Guilarte,

Muñoz-Castañeda

et al. 2019

Preprint

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We present a detailed study of a generalised one-dimensional Kronig-Penney model using δ-δ potentials. We analyse the band structure and the density of states in two situations. In the first case we consider an infinite array formed by identical δ-δ potentials standing at the linear lattice nodes. This case will be known throughout the paper as the one-species hybrid Dirac comb. We investigate the consequences of adding the δ interaction to the Dirac comb by comparing the band spectra and the density of states of pure Dirac-δ combs and one-species hybrid Dirac combs. Secondly we study the quantum system that arises when the periodic potential is the one obtained from the superposition of two one-species hybrid Dirac combs displaced one with respect to the other and with different couplings. The latter will be known as the two-species hybrid Dirac comb. One of the most remarkable results is the appearance of a curvature change in the band spectrum when the δ couplings are above a critical value.

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“…Eq. ( 46) is generated by the effective mass spatial dependence and is of non-local type [15]. Besides spin-dependent point-like interactions can be realized as the thin magnetized interface in layered system.…”

Section: Discussionmentioning

confidence: 99%

Singular spin-flip interactions for the 1D Schrödinger operator

Kulinskii¹,

Panchenko²

2019

Phys. Scr.

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We consider singular self-adjoint extensions of one-dimensional Schrödinger operator acting in space of two-component wave functions within the framework of the distribution theory [1]. We show that among C 4 -parameter set of boundary conditions with state mixing there is only R 2 -parameter subset compatible with the spin interpretation of the two-component structure of wave function. They can be identified as the point-like spin-momentum (Rashba) interactions. We suggest their physical realizations based on the regularized form of the Hamiltonian with coupling of the electrical field inhomogeneity of a background and spin of a carrier.

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Mass-jump and mass-bump boundary conditions for singular self-adjoint extensions of the Schrödinger operator in one dimension

Cited by 11 publications

References 28 publications

An approximation to the Woods–Saxon potential based on a contact interaction

An approximation to the Woods–Saxon potential based on a contact interaction

Band spectra of periodic hybrid $δ$-$δ^\prime$ structures

Singular spin-flip interactions for the 1D Schrödinger operator

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