Dirac Green function for
                    <i>δ</i>
                    potentials

Charro, E.; Glasser, M. L.; Nieto, L. M.

doi:10.1209/0295-5075/120/30006

Cited by 2 publications

(3 citation statements)

References 43 publications

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“…These solutions may be written as sin s = 0, which coincide with (20b), so that no new solutions for the spectral problem arise from (28). The other two solutions are quadratic as function of the parameters and are rather huge and intractable.…”

Section: Parity and Time Reversal Invariance Extensions Fulfilling (20c)mentioning

confidence: 96%

“…Self-adjoint determinations of the operator −d 2 /dx 2 defined on functions supporting whatever interval, K, in the real line R are used to define the so call contact potentials [26,[28][29][30][31]. These are perturbations of the "free operator" H 0 = −d 2 /dx 2 , which are supported on a single point x 0 ∈ K. Typical examples of contact potentials are the Dirac delta δ(x − x 0 ) or its derivative δ (x − x 0 ), which define Hamiltonians of the type…”

Section: Introductionmentioning

confidence: 99%

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Supersymmetric Partners of the One-Dimensional Infinite Square Well Hamiltonian

et al. 2021

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We find supersymmetric partners of a family of self-adjoint operators which are self-adjoint extensions of the differential operator −d2/dx2 on L2[−a,a], a>0, that is, the one dimensional infinite square well. First of all, we classify these self-adjoint extensions in terms of several choices of the parameters determining each of the extensions. There are essentially two big groups of extensions. In one, the ground state has strictly positive energy. On the other, either the ground state has zero or negative energy. In the present paper, we show that each of the extensions belonging to the first group (energy of ground state strictly positive) has an infinite sequence of supersymmetric partners, such that the ℓ-th order partner differs in one energy level from both the (ℓ−1)-th and the (ℓ+1)-th order partners. In general, the eigenvalues for each of the self-adjoint extensions of −d2/dx2 come from a transcendental equation and are all infinite. For the case under our study, we determine the eigenvalues, which are also infinite, all the extensions have a purely discrete spectrum, and their respective eigenfunctions for all of its ℓ-th supersymmetric partners of each extension.

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Section: Parity and Time Reversal Invariance Extensions Fulfilling (20c)mentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Supersymmetric Partners of the One-Dimensional Infinite Square Well Hamiltonian

et al. 2021

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“…Proceeding in a similar way for the analysis of the scattering of positrons by two d-impurities (systems (C.6)-(C.7) in the Appendix C) provides the following scattering amplitudes for positrons: [233,234]. The Green's function solution of the equation…”

Section: Electron and Positron Scattering Spinors: The Continuous Spe...mentioning

confidence: 99%

Extended objects in quantum field theory in three dimensions and applications

Sanz¹

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Faculty of Sciences DEPARTMENT OF THEORETICAL PHYSICS, ATOMIC PHYSICS AND OPTICS Doctor of Philosophy EXTENDED OBJECTS IN QUANTUM FIELD THEORY IN THREE DIMENSIONS AND APPLICATIONS by Lucía SANTAMARÍA SANZ In this thesis the systematic study of Quantum Field Theories (QFT) in various dimensions is proposed from the point of view of mathematical and theoretical physics, paying special attention to systems of one and three spatial dimensions (in addition to the temporal dimension in both cases) under the influence of some particular external conditions. These conditions vary from local interactions with other external classical fields to ideal boundary conditions in confining geometries. More specifically, the main objective of this work is the study of the spectrum of quantum fluctuations of the fields in the vacuum state subject to the external conditions already indicated. This study will be applied to the calculation of several relevant parameters in three-dimensional and one-dimensional extended structures. These systems have recently received increasing interest in material physics (in micro-electromechanical devices based on the Casimir effect or topological defects in meta materials and nano tubes) and in fundamental physics (quantum effects in modern cosmology and topological defects such as domain walls, monopoles and skyrmions). Different configurations of quantum fields, both in compact domains and in open ones with boundaries, will be studied: A scalar field confined between plates mimicked by the most general type of lossless and frequently independent boundary conditions. Scalar fields propagating at finite temperature under the influence of Dirac d-d 0 lattices and Pöschl-Teller combs. Scalar fields between two parallel plates mimicked by Dirac d potentials in a curved background of a topological Pöschl-Teller kink. Relativistic fermionic particles propagating in the real space under the influence of either a single and a double Dirac d potential.

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Dirac Green function for δ potentials

Cited by 2 publications

References 43 publications

Supersymmetric Partners of the One-Dimensional Infinite Square Well Hamiltonian

Supersymmetric Partners of the One-Dimensional Infinite Square Well Hamiltonian

Extended objects in quantum field theory in three dimensions and applications

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