scholarly journals DIRAC SPINORS IN SOLENOIDAL FIELD AND SELF-ADJOINT EXTENSIONS OF ITS HAMILTONIAN

2008 ◽  
Vol 23 (26) ◽  
pp. 2177-2188 ◽  
Author(s):  
PULAK RANJAN GIRI
Keyword(s):  
Dirac Equation ◽  
Bound State ◽  
Parameter Family ◽  
Restricted Domain ◽  
Quantization Procedure ◽  
Remarkable Effect ◽  
Scattering State ◽  
Solenoidal Field ◽  
Scaling Anomaly ◽  
Dirac Spinors

We discuss Dirac equation and its solution in the presence of solenoid (infinitely long) field in (3+1) dimensions. Starting with a very restricted domain for the Hamiltonian, we show that a one-parameter family of self-adjoint extensions are necessary to make sure the correct evolution of the Dirac spinors. Within the extended domain bound state (BS) and scattering state (SS) solutions are obtained. We argue that the existence of bound state in such system is basically due to the breaking of classical scaling symmetry by the quantization procedure. A remarkable effect of the scaling anomaly is that it puts an open bound on both sides of the spectrum, i.e. E ∈ (-M, M) for ν2[0, 1)! We also study the issue of relationship between scattering state and bound state in the region ν2 ∈ [0, 1) and recovered the BS solution and eigenvalue from the SS solution.

scholarly journals Spin and pseudospin solutions to Dirac equation and its thermodynamic properties using hyperbolic Hulthen plus hyperbolic exponential inversely quadratic potential

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Ituen B. Okon ◽  
E. Omugbe ◽  
Akaninyene D. Antia ◽  
C. A. Onate ◽  
Louis E. Akpabio ◽  
...  
Keyword(s):  
Dirac Equation ◽  
Thermodynamic Properties ◽  
Energy Equation ◽  
Pseudospin Symmetry ◽  
Spin Symmetry ◽  
Bound State ◽  
Compact Form ◽  
Relativistic Energy ◽  
Quadratic Potential ◽  
Special Cases

AbstractIn this research article, the modified approximation to the centrifugal barrier term is applied to solve an approximate bound state solutions of Dirac equation for spin and pseudospin symmetries with hyperbolic Hulthen plus hyperbolic exponential inversely quadratic potential using parametric Nikiforov–Uvarov method. The energy eigen equation and the unnormalised wave function were presented in closed and compact form. The nonrelativistic energy equation was obtain by applying nonrelativistic limit to the relativistic spin energy eigen equation. Numerical bound state energies were obtained for both the spin symmetry, pseudospin symmetry and the non relativistic energy. The screen parameter in the potential affects the solutions of the spin symmetry and non-relativistic energy in the same manner but in a revised form for the pseudospin symmetry energy equation. In order to ascertain the accuracy of the work, the numerical results obtained was compared to research work of existing literature and the results were found to be in excellent agreement to the existing literature. The partition function and other thermodynamic properties were obtained using the compact form of the nonrelativistic energy equation. The proposed potential model reduces to Hulthen and exponential inversely quadratic potential as special cases. All numerical computations were carried out using Maple 10.0 version and Matlab 9.0 version softwares respectively.

scholarly journals Bound state of solution of Dirac-Coulomb problem with spatially dependent mass

Open Physics ◽  
2014 ◽  
Vol 12 (4) ◽  
Author(s):  
Eser Olğar ◽  
Hayder Dhahir ◽  
Haydar Mutaf
Keyword(s):  
Dirac Equation ◽  
Coulomb Potential ◽  
Mass Function ◽  
Bound State ◽  
Asymptotic Iteration Method ◽  
Bound State Solution ◽  
Function Generator ◽  
Dependent Mass ◽  
And Function ◽  
Position Dependent Mass

AbstractThe bound state solution of Coulomb Potential in the Dirac equation is calculated for a position dependent mass function M(r) within the framework of the asymptotic iteration method (AIM). The eigenfunctions are derived in terms of hypergeometric function and function generator equations of AIM.

EXACT SOLUTIONS OF DIRAC EQUATION FOR A NEW SPHERICALLY ASYMMETRICAL SINGULAR OSCILLATOR

2010 ◽  
Vol 25 (33) ◽  
pp. 2849-2857 ◽  
Author(s):  
GUO-HUA SUN ◽  
SHI-HAI DONG
Keyword(s):  
Dirac Equation ◽  
Vector Potential ◽  
State Energy ◽  
Energy Levels ◽  
Scalar Potential ◽  
Bound State ◽  
Wave Functions ◽  
Bound State Energy ◽  
Exact Bound ◽  
Spinor Wave

In this work we solve the Dirac equation by constructing the exact bound state solutions for a mixing of scalar and vector spherically asymmetrical singular oscillators. This is done provided that the vector potential is equal to the scalar potential. The spinor wave functions and bound state energy levels are presented. The case V(r) = -S(r) is also considered.

scholarly journals QUANTIZATION OF EXCITON IN MAGNETIC FIELD BACKGROUND

2009 ◽  
Vol 24 (04) ◽  
pp. 321-329
Author(s):  
PULAK RANJAN GIRI ◽  
S. K. CHAKRABARTI
Keyword(s):  
Magnetic Field ◽  
Absorption Coefficient ◽  
Bound State ◽  
State Solution ◽  
Optical Absorption Coefficient ◽  
Background Magnetic Field ◽  
Scattering State ◽  
Adjoint Extension ◽  
Fine Tune ◽  
Experimental Absorption

The possible mismatch between the theoretical and experimental absorption edge peaks in semiconductors in a magnetic field background may arise due to the approximation scheme used to analytically calculate the absorption coefficient. As a possible remedy we suggest to consider nontrivial boundary conditions on x–y plane by in-equivalently quantizing the exciton in background magnetic field. This inequivalent quantization is based on von Neumann's method of self-adjoint extension, which is characterized by a parameter Σ. We obtain bound state solution and scattering state solution, which in general depend upon the self-adjoint extension parameter Σ. The parameter Σ can be used to fine tune the optical absorption coefficient K(Σ) to match with the experiment.

scholarly journals Analytical solution of energy eigen value, eigen function and angular wave function of Dirac equation with Rosen Morse plus Rosen Morse potential in terms of Romanovski polynomials for exact spin symmetry

2017 ◽  
Vol 1 (1) ◽  
pp. 1
Author(s):  
Ihtiari Prasetyaningrum ◽  
C Cari ◽  
A Suparmi
Keyword(s):  
Dirac Equation ◽  
Morse Potential ◽  
State Energy ◽  
Spin Symmetry ◽  
Bound State ◽  
Bound State Energy ◽  
Eigenvalues And Eigenfunctions ◽  
Energy Eigenvalues ◽  
Eigen Value ◽  
Energy Eigenvalues And Eigenfunctions

<p class="Abstract">The energy eigenvalues and eigenfunctions of Dirac equation for Rosen Morse plus Rosen Morse potential are investigated numerically in terms of finite Romanovsky Polynomial. The bound state energy eigenvalues are given in a closed form and corresponding eigenfunctions are obtained in terms of Romanovski polynomials. The energi eigen value is solved by numerical method with Matlab 2011.</p>

Bound state solutions of the Dirac equation for the generalized Cornell potential model

2021 ◽  
Author(s):  
M. Abu-Shady ◽  
E. M. Khokha
Keyword(s):  
Dirac Equation ◽  
Mass Spectra ◽  
Potential Model ◽  
Spin Symmetry ◽  
Bound State ◽  
Energy Eigenvalues ◽  
Cornell Potential ◽  
Modified Kratzer Potential ◽  
Quadratic Potentials ◽  
Light Mesons

In this study, the bound state solutions of the Dirac equation (DE) have been determined with the generalized Cornell potential model (GCPM) under the condition of spin symmetry. The GCPM includes the Cornell potential plus a combination of the harmonic and inversely quadratic potentials. In the framework of the Nikiforov–Uvarov (NU) method, the relativistic and nonrelativistic energy eigenvalues for the GCPM have been obtained. The energies spectra of the Kratzer potential (KP) and the modified Kratzer potential (MKP) have been derived as particular cases of the GCPM. The present results have been applied to some diatomic molecules (DMs) as well as heavy and heavy-light mesons. The energy eigenvalues of the KP and MKP have been computed for several DMs, and they are fully consistent with the results found in the literature. In addition, the energy eigenvalues of the GCPM have been employed for predicting the spin-averaged mass spectra of heavy and heavy-light mesons. One can note that our predictions are in close agreement with the experimental data as well as enhanced compared to the recent studies.

Sign in / Sign up

Export Citation Format

Share Document