scholarly journals ON THE COMMON LIMIT OF THE PT-SYMMETRIC ROSEN–MORSE II AND FINITE SQUARE WELL POTENTIALS

2017 ◽  
Vol 57 (6) ◽  
pp. 412
Author(s):  
József Kovács ◽  
Géza Lévai
Keyword(s):  
Energy Spectrum ◽  
State Energy ◽  
Mathematical Structure ◽  
Bound State ◽  
Transmission And Reflection Coefficients ◽  
Common Limit ◽  
Symmetric Square ◽  
The Common ◽  
Square Well ◽  
Transmission And Reflection

Two <em>PT</em>-symmetric potentials are compared, which possess asymptotically finite imaginary components: the <em>PT</em>-symmetric Rosen-Morse II and the finite <em>PT</em>-symmetric square well potentials. Despite their different mathematical structure, their shape is rather similar, and this fact leads to similarities in their physical characteristics. Their bound-state energy spectrum was found to be purely real, an this finding was attributed to their <br />asymptotically non-vanishing imaginary potential components. Here the <em>V(x</em>)= <em>γδ</em>(<em>x</em>)+ i2Λ sgn(<em>x</em>) potential is discussed, which can be obtained as the common limit of the two other potentials. The energy spectrum, the bound-state wave functions and the transmission and reflection coefficients are studied in the respective limits, and the results are compared.

scholarly journals Bound states of Newton’s equivalent finite square well

2018 ◽  
Vol 33 (33) ◽  
pp. 1850195
Author(s):  
Amornthep Tita ◽  
Pichet Vanichchapongjaroen
Keyword(s):  
Energy Spectrum ◽  
Bound States ◽  
Infinite Order ◽  
State Energy ◽  
Order Differential Equation ◽  
Bound State ◽  
Wave Functions ◽  
Bound State Energy ◽  
Standard Quantum ◽  
Square Well

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.

scholarly journals Quantum star-graph analogues of PT-symmetric square wells

2012 ◽  
Vol 90 (12) ◽  
pp. 1287-1293 ◽  
Author(s):  
Miloslav Znojil
Keyword(s):  
Boundary Conditions ◽  
Bound State ◽  
Robin Boundary Conditions ◽  
Star Graph ◽  
The Real ◽  
Rotation Symmetric ◽  
Symmetric Quantum ◽  
Symmetric Square ◽  
Square Well ◽  
Robin Boundary

We recall the solvable [Formula: see text]-symmetric quantum square well on an interval of x ∈ (–L, L) := [Formula: see text] (with an α-dependent non-Hermiticity given by Robin boundary conditions) and generalize it. In essence, we just replace the support interval [Formula: see text] (reinterpreted as an equilateral two-pointed star graph with Kirchhoff matching at the vertex x = 0) with a q-pointed equilateral star graph [Formula: see text] endowed with the simplest complex-rotation-symmetric external α-dependent Robin boundary conditions. The remarkably compact form of the secular determinant is then deduced. Its analysis reveals that (i) at any integer q = 2, 3, …, there exists the same q-independent and infinite subfamily of the real energies, and (ii) at any special q = 2, 6, 10, …, there exists another, additional, q-dependent infinite subfamily of the real energies. In the spirit of the recently proposed dynamical construction of the Hilbert space of a quantum system, the physical bound-state interpretation of these eigenvalues is finally proposed.

scholarly journals Pseudo-spin Symmetry in Dirac-Four-Parameter Diatomic Problem Coupled with a Coulomb-like Tensor potential

BIBECHANA ◽  
2012 ◽  
Vol 8 ◽  
pp. 23-30
Author(s):  
Mahdi Eshghi
Keyword(s):  
Energy Spectrum ◽  
Dirac Equation ◽  
State Energy ◽  
Spin Symmetry ◽  
Bound State ◽  
Wave Functions ◽  
Bound State Energy ◽  
Tensor Potential ◽  
Uvarov Method ◽  
Spinor Wave

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

scholarly journals Quasi-bound states in an NPN-type nanometer-scale graphene quantum dot under a magnetic field

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Yueting Pan ◽  
Haijiao Ji ◽  
Xin-Qi Li ◽  
Haiwen Liu
Keyword(s):  
Magnetic Field ◽  
Energy Spectrum ◽  
Quantum Dot ◽  
State Energy ◽  
Bound State ◽  
Scanning Tunneling ◽  
Bound State Energy ◽  
Graphene Quantum Dot ◽  
The Magnetic Field ◽  
Quasi Bound State

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.

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
Keyword(s):  
Energy Spectrum ◽  
Continuous Spectrum ◽  
Bound States ◽  
State Energy ◽  
Band System ◽  
Bound State ◽  
Flat Band ◽  
Bound State Energy ◽  
Type Iii ◽  
Potential Strength

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.

Lower Bound for ppK– Quasi-Bound State Energy

2020 ◽  
Vol 51 (5) ◽  
pp. 979-987 ◽  
Author(s):  
I. Filikhin ◽  
B. Vlahovic
Keyword(s):  
Lower Bound ◽  
State Energy ◽  
Bound State ◽  
Bound State Energy ◽  
Quasi Bound State

scholarly journals Transmission, Reflection and Dissipation of Microwaves in Magnetic Composites with Nanocrystalline Finemet-Type Flakes

Materials ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 3499
Author(s):  
Anatoly B. Rinkevich ◽  
Dmitry V. Perov ◽  
Yuriy I. Ryabkov
Keyword(s):  
Composite Material ◽  
Microwave Absorption ◽  
Nanocrystalline Alloy ◽  
Reflection Coefficients ◽  
Magnetic Composites ◽  
Transmission And Reflection Coefficients ◽  
Wave Interference ◽  
Microwave Losses ◽  
Frequency Dependences ◽  
Transmission And Reflection

The microwave properties of a composite material containing flakes of finemet-type nanocrystalline alloy placed in the epoxy matrix have been investigated. Two compositions have been studied: with 15% and 30% flakes. Frequency dependences of transmission and reflection coefficients are measured in the frequency range from 12 to 38 GHz. The dielectric permittivity and magnetic permeability are obtained, and the microwave losses are calculated. The dependences of transmission and reflection coefficients have been drawn as functions of wave frequency and thickness of the composite material, taking into account the frequency dependences of permittivity and permeability. The regions of maximal and minimal microwave absorption have been defined. The influence of wave interference on the frequency dependence of microwave absorption is studied.

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