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 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.

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.

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 Shannon entropy for Feinberg–Horodecki equation and thermal properties of improved Wei potential model

Open Physics ◽  
2021 ◽  
Vol 19 (1) ◽  
pp. 519-533
Author(s):  
Clement Atachegbe Onate ◽  
Michael Chukwudi Onyeaju ◽  
Ituen Bassey Okon
Keyword(s):  
Thermodynamic Properties ◽  
Shannon Entropy ◽  
Energy Equation ◽  
Potential Model ◽  
Wave Functions ◽  
Vibrational Entropy ◽  
Position Space ◽  
Energy Potential ◽  
One Dimensional ◽  
Uvarov Method

Abstract We solved a one-dimensional time-dependent Feinberg–Horodecki equation for an improved Wei molecular energy potential function using the parametric Nikiforov–Uvarov method. The quantized momentum and the corresponding wave functions were obtained. With the help of the wave functions obtained, we calculated Shannon entropy for both the position space and momentum space. The results were used to study four molecules. The results of Shannon entropy were found to be in excellent agreement with those found in the literature. For more usefulness of these studies, the quantized momentum obtained was transformed into an energy equation with certain transformations. The energy equation was then used to calculate some thermodynamic properties such as vibrational mean energy, vibrational specific heat, vibrational mean free energy, and vibrational entropy via computation of the partition function. The thermodynamic properties studied for CO, NO, CH, and ScH showed that for a certain range of the temperature studied, the molecules exhibited similar features except for the vibrational entropy.

scholarly journals NEW TREATMENT OF THE NONCOMMUTATIVE DIRAC EQUATION WITH A COULOMB POTENTIAL

2012 ◽  
Vol 27 (19) ◽  
pp. 1250100 ◽  
Author(s):  
LAMINE KHODJA ◽  
SLIMANE ZAIM
Keyword(s):  
Magnetic Field ◽  
Field Equation ◽  
Hydrogen Atom ◽  
Dirac Equation ◽  
Hyperfine Structure ◽  
Coulomb Potential ◽  
Energy Levels ◽  
Nonrelativistic Limit ◽  
New Treatment

Using the approach of the modified Euler–Lagrange field equation together with the corresponding Seiberg–Witten maps of the dynamical fields, a noncommutative Dirac equation with a Coulomb potential is derived. We then find the noncommutative modification to the energy levels and the possible new transitions. In the nonrelativistic limit a general form of the Hamiltonian of the hydrogen atom is obtained, and we show that the noncommutativity plays the role of spin and magnetic field which gives the hyperfine structure.

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.

Dirac equation with CPRS potential and Cornell tensor interaction in the presence of spin and pseudospin symmetry

2020 ◽  
Vol 29 (08) ◽  
pp. 2050064
Author(s):  
Parisa Sedaghatnia ◽  
Hassan Hassanabadi ◽  
Marc de Montigny
Keyword(s):  
Dirac Equation ◽  
Nuclear Physics ◽  
Energy Levels ◽  
Pseudospin Symmetry ◽  
Tensor Interaction ◽  
Wave Functions ◽  
Nuclear Spectroscopy ◽  
Exactly Solvable

Motivated by the prominent role of tensor interactions in nuclear spectroscopy and many applications of spin and pseudospin symmetry in hadronic and nuclear physics, we solve the Dirac equation with a CPRS potential and a Cornell tensor interaction, in the spin and pseudospin symmetry limits, by using the quasi-exactly solvable method. We obtain explicitly the wave functions for the two lowest energy levels, both for spin and pseudospin symmetry. We also discuss the degeneracy of the system.

scholarly journals Energy States of Some Diatomaic Molecules: The Exact Quantisation Rule Approach

2015 ◽  
Vol 70 (2) ◽  
pp. 85-90 ◽  
Author(s):  
Babatunde J. Falaye ◽  
Sameer M. Ikhdair ◽  
Majid Hamzavi
Keyword(s):  
Hypergeometric Functions ◽  
Vibrational Energy ◽  
Energy Levels ◽  
Wave Functions ◽  
Energy Eigenvalues ◽  
Molecular Potential ◽  
Approximate Analytical Solutions ◽  
Rule Approach ◽  
Radial Schrödinger Equation ◽  
Good Agreement

AbstractIn this study, we obtain the approximate analytical solutions of the radial Schrödinger equation for the Deng–Fan diatomic molecular potential by using the exact quantisation rule approach. The wave functions were expressed by hypergeometric functions via the functional analysis approach. An extension to the rotational–vibrational energy eigenvalues of some diatomic molecules is also presented. It is shown that the calculated energy levels are in good agreement with those obtained previously (Enℓ–D; shifted Deng–Fan).

scholarly journals Comment on “Solutions of the Dirac equation with an improved expression of the Rosen–Morse potential energy model including Coulomb-like tensor interaction”

2019 ◽  
Vol 97 (10) ◽  
pp. 1167-1169
Author(s):  
S. Bouledjedj ◽  
A. Khodja ◽  
F. Benamira ◽  
L. Guechi
Keyword(s):  
Dirac Equation ◽  
Morse Potential ◽  
Bound States ◽  
Hypergeometric Functions ◽  
Energy Levels ◽  
Transcendental Equation ◽  
Tensor Interaction ◽  
Polynomial Method ◽  
Generalized Hypergeometric Functions ◽  
Spinor Wave

The Nikiforov–Uvarov polynomial method employed by Aguda (Can. J. Phys. 2013, 91: 689. doi: 10.1139/cjp-2013-0109 ) to solve the Dirac equation with an improved Rosen–Morse potential plus a Coulomb-like tensor potential is shown to be inappropriate because the conditions of its application are not fulfilled. We clarify the problem and construct the correct solutions in the spin and pseudospin symmetric regimes via the standard method of solving differential equations. For the bound states, we obtain the spinor wave functions in terms of the generalized hypergeometric functions 2F1(a, b, c; z) and in each regime we show that the energy levels are determined by the solutions of a transcendental equation that can be solved numerically.

Analytical solution of the Duffin - Kemmer - Petiau equation for the sum of the Manning - Rosen and the Yukawa class potential

2021 ◽  
pp. 140-150
Author(s):  
S.M. Aslanova ◽  
Keyword(s):  
Hypergeometric Functions ◽  
Energy Levels ◽  
Energy Eigenvalue ◽  
Bound State ◽  
Wave Functions ◽  
State Solution ◽  
Bound State Solution ◽  
Radial Wave ◽  
Quantum Numbers ◽  
Analytical Expressions

This paper presents an analytical bound-state solution to the Duffin - Kemmer - Petiau equation for the new putative combined Manning - Rosen and Yukawa class potentials. Using the developed scheme to approximate and overcome the difficulties arising in the centrifugal part of the potential, the bound-state solution of the modified Duffin - Kemmer - Petiau equation is found. Analytical expressions of energy eigenvalue and the corresponding radial wave functions are obtained for an arbitrary value of the orbital quantum number l . Also, eigenfunctions are expressed in terms of hypergeometric functions. It is shown that energy levels and eigenfunctions are quite sensitive to the choice of radial and orbital quantum numbers.

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