Infinite bound states and $1/n$ energy spectrum induced by a Coulomb-like potential of type III in a flat band system

2021 ◽  
Author(s):  
Yi-Cai Zhang

Abstract In this work, we investigate the bound states in a one-dimensional spin-1 flat band system with a Coulomb-like potential of type III, which has a unique non-vanishing matrix element in basis $|1\rangle$. It is found that, for such a kind of potential, there exists infinite bound states. Near the threshold of continuous spectrum, the bound state energy is consistent with the ordinary hydrogen-like atom energy level with Rydberg correction. In addition, the flat band has significant effects on the bound states. For example, there are infinite bound states which are generated from the flat band. Furthermore, when the potential is weak, the bound state energy is proportional to the potential strength $\alpha$. When the bound state energies are very near the flat band, they are inversely proportional to the natural number $n$ (e.g., $E_n\propto 1/n, n=1,2,3,...$). Further we find that the energy spectrum can be well described by quasi-classical approximation (WKB method). Finally, we give a critical potential strength $\alpha_c$ at which the bound state energy reaches the threshold of continuous spectrum. After crossing the threshold, the bound states in the continuum (BIC) would exist in such a flat band system.

2018 ◽  
Vol 33 (33) ◽  
pp. 1850195
Author(s):  
Amornthep Tita ◽  
Pichet Vanichchapongjaroen

In this paper, a one-parameter family of Newton’s equivalent Hamiltonians (NEH) for finite square well potential is analyzed in order to obtain bound state energy spectrum and wave functions. For a generic potential, each of the NEH is classically equivalent to one another and to the standard Hamiltonian yielding Newton’s equations. Quantum mechanically, however, they are expected to be different from each other. The Schrödinger’s equation coming from each NEH with finite square well potential is an infinite order differential equation. The matching conditions, therefore, demand the wave functions to be infinitely differentiable at the well boundaries. To handle this, we provide a way to consistently truncate these conditions. It turns out as expected that bound state energy spectrum and wave functions are dependent on the parameter [Formula: see text] which is used to characterize different NEH. As [Formula: see text], the energy spectrum coincides with that from the standard quantum finite square well.


2019 ◽  
Vol 34 (27) ◽  
pp. 1950220
Author(s):  
F. Chezani Sharahi ◽  
M. Monemzadeh ◽  
A. Abdoli Arani

In this study, the bound state energy of a four-quark system was analytically calculated as a two heavy–heavy anti-quarks [Formula: see text] and two light–light quarks [Formula: see text]. Tetraquark was assumed to be a bound state of two-body system consisting of two mesons, each containing a light quark and a heavy antiquark. Due to the presence of heavy mesons in the tetraquark, Born–Oppenheimer approximation was used to study its bound states. To assess the bounding energy, Schrödinger equation was solved using lattice QCD [Formula: see text] potential, having expanded the tetraquark potential [Formula: see text] up to 11th term. Binding energy state and wave function, however, were obtained in the scalar [Formula: see text] channel. Graphical results for wave functions obtained versus antiquark–antiquark distance [Formula: see text] confirmed the existence of the tetraquark [Formula: see text]. Analytical bound state energy obtained here was in good agreement with several numerical ones published in the literature, confirming the accuracy of the approach taken here.


1989 ◽  
Vol 01 (01) ◽  
pp. 139-146 ◽  
Author(s):  
SHAO-JING DONG ◽  
CHEN NING YANG

The bound state energy and wave function for two particles in a 2- or 3-dimensional infinite lattice with attractive Kronecker δ-function interaction are discussed.


BIBECHANA ◽  
2012 ◽  
Vol 8 ◽  
pp. 23-30
Author(s):  
Mahdi Eshghi

In this work, we use the parametric generalization of the Nikiforov-Uvarov method to obtain the relativistic bound state energy spectrum and the corresponding spinor wave-functions for four-parameter diatomic potential coupled with a Coulomb-like tensor under the condition of the pseudo-spin symmetry. Also, some numerical results have given.Keywords: Dirac equation; four-parameter diatomic potential; Coulomb-like tensorDOI: http://dx.doi.org/10.3126/bibechana.v8i0.4879BIBECHANA 8 (2012) 23-30


1989 ◽  
Vol 03 (10) ◽  
pp. 813-813
Author(s):  
SHAO-JING DONG ◽  
CHEN NING YANG

The bound state energy and wave function for two particles in a 2- or 3-dimensional infinite lattice with attractive Kronecker δ-function interaction are discussed.


2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Yueting Pan ◽  
Haijiao Ji ◽  
Xin-Qi Li ◽  
Haiwen Liu

AbstractWe solve the quasi-bound state-energy spectra and wavefunctions of an NPN-type graphene quantum dot under a perpendicular magnetic field. The evolution of the quasi-bound state spectra under the magnetic field is investigated using a Wentzel–Kramers–Brillouin approximation. In numerical calculations, we also show that the twofold energy degeneracy of the opposite angular momenta breaks under a weak magnetic field. As the magnetic field strengthens, this phenomenon produces an observable splitting of the energy spectrum. Our results demonstrate the relation between the quasi-bound state-energy spectrum in graphene quantum dots and magnetic field strength, which is relevant to recent measurements in scanning tunneling microscopy.


2020 ◽  
Vol 2 (2) ◽  
Author(s):  
Jean-Damien Pillet ◽  
Vincent Benzoni ◽  
Joël Griesmar ◽  
Jean-Loup Smirr ◽  
Çağlar Girit

An Andreev molecule is a system of closely spaced superconducting weak links accommodating overlapping Andreev Bound States. Recent theoretical proposals have considered one-dimensional Andreev molecules with a single conduction channel. Here we apply the scattering formalism and extend the analysis to multiple conduction channels, a situation encountered in epitaxial superconductor/semiconductor weak links. We obtain the multi-channel bound state energy spectrum and quantify the contribution of the microscopic non-local transport processes leading to the formation of Andreev molecules.


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