scholarly journals Three-Dimensional Dirac Oscillator with Minimal Length: Novel Phenomena for Quantized Energy

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Malika Betrouche ◽  
Mustapha Maamache ◽  
Jeong Ryeol Choi
Keyword(s):  
Energy Spectrum ◽  
Energy Levels ◽  
Three Dimensional ◽  
Nonrelativistic Limit ◽  
Minimal Length ◽  
Wave Functions ◽  
Dirac Oscillator ◽  
Planck Length ◽  
Standard Case ◽  
Small Parameters

We study quantum features of the Dirac oscillator under the condition that the position and the momentum operators obey generalized commutationrelations that lead to the appearance of minimal length with the order of the Planck length,∆xmin=ℏ3β+β′, whereβandβ′are two positive small parameters. Wave functions of the system and the corresponding energy spectrum are derived rigorously. The presence of the minimal length accompanies a quadratic dependence of the energy spectrum on quantum numbern, implying the property of hard confinement of the system. It is shown that the infinite degeneracy of energy levels appearing in the usual Dirac oscillator is vanished by the presence of the minimal length so long asβ≠0. Not only in the nonrelativistic limit but also in the limit of the standard case(β=β′=0), our results reduce to well known usual ones.

Relativistic quantum bouncing particles in a homogeneous gravitational field

2021 ◽  
pp. 2150098
Author(s):  
Ar Rohim ◽  
Kazushige Ueda ◽  
Kazuhiro Yamamoto ◽  
Shih-Yuin Lin
Keyword(s):  
Gravitational Field ◽  
Relativistic Effect ◽  
Relativistic Quantum ◽  
Energy Levels ◽  
Nonrelativistic Limit ◽  
Wave Functions ◽  
Dirac Equations ◽  
Rindler Coordinates ◽  
Klein Gordon ◽  
Homogeneous Gravitational Field

In this paper, we study the relativistic effect on the wave functions for a bouncing particle in a gravitational field. Motivated by the equivalence principle, we investigate the Klein–Gordon and Dirac equations in Rindler coordinates with the boundary conditions mimicking a uniformly accelerated mirror in Minkowski space. In the nonrelativistic limit, all these models in the comoving frame reduce to the familiar eigenvalue problem for the Schrödinger equation with a fixed floor in a linear gravitational potential, as expected. We find that the transition frequency between two energy levels of a bouncing Dirac particle is greater than the counterpart of a Klein–Gordon particle, while both are greater than their nonrelativistic limit. The different corrections to eigen-energies of particles of different nature are associated with the different behaviors of their wave functions around the mirror boundary.

scholarly journals Modeling of circular quantum dots localized in double heterostructures

2021 ◽  
Vol 65 (1) ◽  
pp. 33-39
Author(s):  
V. V. Kudryashov ◽  
A. V. Baran
Keyword(s):  
Quantum Dots ◽  
Energy Spectrum ◽  
Energy Levels ◽  
Finite Depth ◽  
Wave Functions ◽  
Axially Symmetric ◽  
Confinement Potential ◽  
Double Heterostructures ◽  
New Type ◽  
Potential Parameters

The circular quantum dots localized in the double heterostructures are simulated by means of the axially symmetric smooth confinement potential of finite depth. For the proposed potential of new type, the exact wave functions and the energy levels of electron are found. The dependence of energy spectrum on potential parameters is investigated.

Exact solution of the relativistic finite-difference equation for the Coulomb plus a ring-shaped-like potential

2019 ◽  
Vol 34 (17) ◽  
pp. 1950089 ◽  
Author(s):  
Sh. M. Nagiyev ◽  
A. I. Ahmadov
Keyword(s):  
Energy Spectrum ◽  
Finite Difference ◽  
Jacobi Polynomials ◽  
Relativistic Quantum ◽  
Three Dimensional ◽  
Dynamical Symmetry ◽  
Wave Functions ◽  
Relativistic Quantum Mechanics ◽  
Radial Part ◽  
Radial Wave

In this paper, a three-dimensional problem of the motion of a charged relativistic particle in a noncentral Coulomb plus ring-shaped potential is studied. Our investigation is based on a finite-difference version of relativistic quantum mechanics. The energy eigenvalues and the corresponding wave functions are obtained analytically. It is shown that radial part and the angular part of the wave functions are expressed through the Meixner–Pollaczek polynomials and Jacobi polynomials, respectively. All relativistic expressions, for example, radial wave functions and energy spectrum, have the correct nonrelativistic limit. We also build a dynamical symmetry group for the radial part of the equation of motion, which allows us to find the energy spectrum purely algebraically.

scholarly journals SOLUTION OF THE DIRAC EQUATION WITH NONCENTRAL THREE-VECTOR POTENTIAL

2006 ◽  
Vol 21 (07) ◽  
pp. 581-592 ◽  
Author(s):  
A. D. ALHAIDARI
Keyword(s):  
Energy Spectrum ◽  
Dirac Equation ◽  
Vector Potential ◽  
Radial Component ◽  
Wave Functions ◽  
Relativistic Energy ◽  
Dirac Oscillator ◽  
Spherical Coordinates ◽  
The One ◽  
Spinor Wave

We introduce coupling to three-vector potential in the (3+1)-dimensional Dirac equation. The potential is noncentral (angular-dependent) such that the Dirac equation separates completely in spherical coordinates. The relativistic energy spectrum and spinor wave functions are obtained for the case where the radial component of the vector potential is proportional to 1/r. The coupling presented in this work is a generalization of the one which was introduced by Moshinsky and Szczepaniak for the Dirac-oscillator problem.

Theoretical studies in nuclear structure III. Radial integrals for the nuclear s, p and d shells

1951 ◽  
Vol 205 (1081) ◽  
pp. 238-246 ◽  
Keyword(s):  
Nuclear Structure ◽  
Interaction Potential ◽  
Nuclear Energy ◽  
Energy Levels ◽  
Three Dimensional ◽  
Wave Functions ◽  
Theoretical Studies ◽  
Hartree Approximation ◽  
Radial Wave ◽  
Working Out

In working out nuclear energy levels on the Hartree approximation one meets certain integrals involving the interaction potential and the particle radial wave-functions (see parts I and II by H. A. Jahn (1950, 1951) in the present series). In this note these integrals are defined and worked out for the 1 s , 2 p , 3 d wave-functions of a three-dimensional oscillator using as interaction potential ( a ) the Gauss potential, ( b ) the meson potential.

scholarly journals λϕ4 KINK AND SINE-GORDON SOLITON IN THE GUP FRAMEWORK

2014 ◽  
Vol 23 (04) ◽  
pp. 1450039 ◽  
Author(s):  
M. ASGHARI ◽  
P. PEDRAM
Keyword(s):  
Differential Equation ◽  
Energy Spectrum ◽  
Fourth Order ◽  
Order Differential Equation ◽  
Dominant Role ◽  
Minimal Length ◽  
Planck Length ◽  
Generalized Schrödinger Equation ◽  
Discrete States ◽  
Fourth Order Differential Equation

We consider λϕ4 kink and sine-Gordon soliton in the presence of a minimal length uncertainty proportional to the Planck length. The modified Hamiltonian contains an extra term proportional to p4 and the generalized Schrödinger equation is expressed as a fourth-order differential equation in quasiposition space. We obtain the modified energy spectrum for the discrete states and compare our results with one-loop resummed and Hartree approximations for the quantum fluctuations. We finally find some lower bounds for the deformations parameter, so that the effects of the minimal length have the dominant role.

scholarly journals Relativistic and nonrelativistic solutions of the generalized Pöschl–Teller and hyperbolical potentials with some thermodynamic properties

2015 ◽  
Vol 24 (03) ◽  
pp. 1550020 ◽  
Author(s):  
C. A. Onate ◽  
J. O. Ojonubah
Keyword(s):  
Dirac Equation ◽  
Thermodynamic Properties ◽  
Hypergeometric Functions ◽  
Energy Equation ◽  
Energy Levels ◽  
Nonrelativistic Limit ◽  
Wave Functions ◽  
Approximation Type ◽  
Supersymmetric Approach

By using the new approximation type, the Dirac equation is solved with the combination of Generalized Pöschl–Teller and Hyperbolical potentials within the framework of supersymmetric approach. The energy levels are obtained for both pseudospin and spin symmetries and the nonrelativistic limit is obtained with the corresponding wave functions in terms of hypergeometric functions. Some thermodynamic properties are equally obtained with the energy equation of the nonrelativistic limit.

scholarly journals MATLAB Wavelet analysis of electron energy spectrum in one-dimensional quantum well with infinitely high walls for Al-Ga-As system (0 < x < 1)

2021 ◽  
Vol 2056 (1) ◽  
pp. 012025
Author(s):  
E R Kozhanova ◽  
I M Tkachenko ◽  
V V Belyaev ◽  
S Maignan
Keyword(s):  
Energy Spectrum ◽  
Quantum Well ◽  
Energy Levels ◽  
Electronic States ◽  
Semiconductor Nanostructures ◽  
Electron Energy Spectrum ◽  
Wave Functions ◽  
Quantum Energy ◽  
One Dimensional ◽  
Analysis Of Results

Abstract This paper presents calculations of electronic states in AlxGa1-x As semiconductor nanostructures and simulates the envelope wave functions of quantum energy levels in a one-dimensional quantum well with infinitely high walls of a given width at various values of x. For the analysis of results the authors choose the function wtmm from the Matlab library that fixes the extremums and which is a characteristic of the fractality of the envelope wave functions of quantum energy levels.

scholarly journals The exact solutions of a (2 + 1)-dimensional Dirac oscillator under a magnetic field in the presence of a minimal length

2015 ◽  
Vol 93 (5) ◽  
pp. 542-548 ◽  
Author(s):  
Abdelmalek Boumali ◽  
Hassan Hassanabadi
Keyword(s):  
Magnetic Field ◽  
Exact Solutions ◽  
Momentum Space ◽  
Uniform Magnetic Field ◽  
Hypergeometric Functions ◽  
Minimal Length ◽  
Wave Functions ◽  
Two Dimensional ◽  
Dirac Oscillator ◽  
Energy Eigenvalues

Minimal length of a two-dimensional Dirac oscillator is investigated in the presence of a uniform magnetic field and illustrates the wave functions in the momentum space. The energy eigenvalues are found and the corresponding wave functions are calculated in terms of hypergeometric functions.

NEW TYPE SHIFT OPERATORS FOR THREE-DIMENSIONAL INFINITE WELL POTENTIAL

2011 ◽  
Vol 26 (05) ◽  
pp. 351-358 ◽  
Author(s):  
GUO-HUA SUN ◽  
SHI-HAI DONG
Keyword(s):  
Energy Spectrum ◽  
Three Dimensional ◽  
Quantum Systems ◽  
Wave Functions ◽  
Shift Operators ◽  
New Type ◽  
Type Shift

New type shift operators for three-dimensional infinite well potential are identified to connect those quantum systems with different radials R but with the same energy spectrum. It should be pointed out that these shift operators depend on all variables contained in wave functions. Thus they establish a novel relation between wave functions ψlm(r) and ψ(l±1)(m±1)(r).

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