scholarly journals Comment on “Bound states and the potential parameter spectrum” [J. Math. Phys. 61, 062103 (2020)]

2021 ◽  
Vol 62 (6) ◽  
pp. 064101
Author(s):  
Francisco M. Fernández
Keyword(s):  
Bound States ◽  
Potential Parameter ◽  
Math Phys

scholarly journals The spectrum of the Schrödinger–Hamiltonian for trapped particles in a cylinder with a topological defect perturbed by two attractive delta interactions

2018 ◽  
Vol 15 (08) ◽  
pp. 1850135 ◽  
Author(s):  
Fassari Silvestro ◽  
Rinaldi Fabio ◽  
Viaggiu Stefano
Keyword(s):  
Quantum Dot ◽  
Harmonic Oscillator ◽  
Total Energy ◽  
Spectral Properties ◽  
Bound States ◽  
Three Dimensional ◽  
Point Interactions ◽  
One Dimensional ◽  
The One ◽  
Math Phys

In this paper, we exploit the technique used in [Albeverio and Nizhnik, On the number of negative eigenvalues of one-dimensional Schrödinger operator with point interactions, Lett. Math. Phys. 65 (2003) 27; Albeverio, Gesztesy, Hoegh-Krohn and Holden, Solvable Models in Quantum Mechanics (second edition with an appendix by P. Exner, AMS Chelsea Series 2004); Albeverio and Kurasov, Singular Perturbations of Differential Operators: Solvable Type Operators (Cambridge University Press, 2000); Fassari and Rinaldi, On the spectrum of the Schrödinger–Hamiltonian with a particular configuration of three one-dimensional point interactions, Rep. Math. Phys. 3 (2009) 367; Fassari and Rinaldi, On the spectrum of the Schrödinger–Hamiltonian of the one-dimensional harmonic oscillator perturbed by two identical attractive point interactions, Rep. Math. Phys. 3 (2012) 353; Albeverio, Fassari and Rinaldi, The Hamiltonian of the harmonic oscillator with an attractive-interaction centered at the origin as approximated by the one with a triple of attractive-interactions, J. Phys. A: Math. Theor. 49 (2016) 025302; Albeverio, Fassari and Rinaldi, Spectral properties of a symmetric three-dimensional quantum dot with a pair of identical attractive [Formula: see text]-impurities symmetrically situated around the origin II, Nanosyst. Phys. Chem. Math. 7(5) (2016) 803; Albeverio, Fassari and Rinaldi, Spectral properties of a symmetric three-dimensional quantum dot with a pair of identical attractive [Formula: see text]-impurities symmetrically situated around the origin, Nanosyst. Phys. Chem. Math. 7(2) (2016) 268] to deal with delta interactions in a rigorous way in a curved spacetime represented by a cosmic string along the [Formula: see text] axis. This mathematical machinery is applied in order to study the discrete spectrum of a point-mass particle confined in an infinitely long cylinder with a conical defect on the [Formula: see text] axis and perturbed by two identical attractive delta interactions symmetrically situated around the origin. We derive a suitable approximate formula for the total energy. As a consequence, we found the existence of a mixing of states with positive or zero energy with the ones with negative energy (bound states). This mixture depends on the radius [Formula: see text] of the trapping cylinder. The number of quantum bound states is an increasing function of the radius [Formula: see text]. It is also interesting to note the presence of states with zero total energy (quasi free states). Apart from the gravitational background, the model presented in this paper is of interest in the context of nanophysics and graphene modeling. In particular, the graphene with double layer in this framework, with the double layer given by the aforementioned delta interactions and the string on the [Formula: see text]-axis modeling topological defects connecting the two layers. As a consequence of these setups, we obtain the usual mixture of positive and negative bound states present in the graphene literature.

scholarly journals Bound states and the potential parameter spectrum

2020 ◽  
Vol 61 (6) ◽  
pp. 062103
Author(s):  
A. D. Alhaidari ◽  
H. Bahlouli
Keyword(s):  
Bound States ◽  
Potential Parameter

scholarly journals A complete classification of threshold properties for one-dimensional discrete Schrödinger operators

2015 ◽  
Vol 27 (01) ◽  
pp. 1550002 ◽  
Author(s):  
Kenichi Ito ◽  
Arne Jensen
Keyword(s):  
Bound States ◽  
Complete Classification ◽  
Full Generality ◽  
One Dimensional ◽  
All Solutions ◽  
Growth Properties ◽  
Discrete Schrödinger Operators ◽  
The One ◽  
Math Phys ◽  
Generalized Zero

We consider the one-dimensional discrete Schrödinger operator on ℤ, and study the relation between the generalized eigenstates and the asymptotic expansion of the resolvent for the threshold 0. We decompose the generalized zero eigenspace into subspaces, some of which correspond to the bound states or the resonance states, only by their growth properties at infinity, and precisely describe the first few leading coefficients in the expansion using these subspaces. The generalized zero eigenspace we consider is the largest possible one, consisting of all solutions to the eigenequation. For the resolvent expansion, we implement the expansion scheme of Jensen–Nenciu [Rev. Math. Phys. 13 (2001) 717–754] and [Rev. Math. Phys. 16 (2004) 675–677] in its full generality.

Recent Radiative and Collisional Atomic Data of Astrophysical Interest

1988 ◽  
Vol 102 ◽  
pp. 129-132
Author(s):  
K.L. Baluja ◽  
K. Butler ◽  
J. Le Bourlot ◽  
C.J. Zeippen
Keyword(s):  
Mass Production ◽  
Bound States ◽  
Physical Models ◽  
Impact Excitation ◽  
Electron Impact Excitation ◽  
Atomic Data ◽  
Isoelectronic Sequence ◽  
Astrophysical Interest ◽  
Radiative Transitions ◽  
Forbidden Transitions

SummaryUsing sophisticated computer programs and elaborate physical models, accurate radiative and collisional atomic data of astrophysical interest have been or are being calculated. The cases treated include radiative transitions between bound states in the 2p4and 2s2p5configurations of many ions in the oxygen isoelectronic sequence, the photoionisation of the ground state of neutral iron, the electron impact excitation of the fine-structure forbidden transitions within the 3p3ground configuration of CℓIII, Ar IV and K V, and the mass-production of radiative data for ions in the oxygen and fluorine isoelectronic sequences, as part of the international Opacity Project.

Spectrum of Bound States of Nucleus 10B in a Three-Cluster Microscopic Model

2014 ◽  
Vol 59 (11) ◽  
pp. 1065-1077 ◽  
Author(s):  
A.V. Nesterov ◽  
◽  
V.S. Vasilevsky ◽  
T.P. Kovalenko ◽  
◽  
...  
Keyword(s):  
Bound States ◽  
Microscopic Model
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