2019
DOI: 10.1016/j.aop.2018.11.017
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Hyperspherical δ-δ potentials

Abstract: The spherically symmetric potential a δ(r − r 0 ) + b δ (r − r 0 ) is generalised for the ddimensional space as a characterisation of a unique selfadjoint extension of the free Hamiltonian. For this extension of the Dirac delta, the spectrum of negative, zero and positive energy states is studied in d ≥ 2, providing numerical results for the expectation value of the radius as a function of the free parameters of the potential. Remarkably, only if d = 2 the δ-δ potential for arbitrary a > 0 admits a bound state… Show more

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Cited by 17 publications
(18 citation statements)
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“…where the equality follows from standard properties of the Bessel functions [59] and the second relation from the Turan-type inequalities [50,70]:…”
Section: Discussionmentioning
confidence: 99%
See 1 more Smart Citation
“…where the equality follows from standard properties of the Bessel functions [59] and the second relation from the Turan-type inequalities [50,70]:…”
Section: Discussionmentioning
confidence: 99%
“…(15). These requirements are given by matching conditions relating the function u (r ) and its first derivative at the limit values of R. They can be written in terms of a SL(2, R) matrix as [14,15,50,51]…”
Section: Matching Conditionsmentioning
confidence: 99%
“…We are going to consider now an extension of the previous study of two interacting particles that takes into account the presence of an extra point-like interaction term in the potential, proportional to δ . This type of point or zerorange potentials are a subject of recent study in differents contexts [30][31][32][33]. The Hamiltonian of the light particle with mass m is now given for t < 0 by…”
Section: B Case Of Two Particles Interacting Through a δ-δ Interactionmentioning
confidence: 99%
“…2. In addition, the whole interaction defined in this way can be seen as a generalization of the Robin boundary conditions, which are obtained as a finite limit case [21]. Within this framework, the δ-δ interaction is introduced by imposing appropriate matching conditions for the radial wave functions at the radius R.…”
Section: Introductionmentioning
confidence: 99%