Approximate Solutions of Dirac Equation with Hyperbolic-Type Potential

Arda, Altuğ; Sever, R.

doi:10.1088/0253-6102/64/3/269

Cited by 8 publications

(3 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…have been applied. In this investigations various kinds of potentials including the harmonic oscillator potential [14], Eckart potential [15,11], Woods-Saxon potential [6], Hyperbolic-type potential [16], scalar or vector potential (linear and/or of Coulomb-type) have been considered.…”

Section: Introductionmentioning

confidence: 99%

The Dirac equation in (1 + 2) -dimensional Gürses space-time backgrounds

Ahmed

2019

Eur. Phys. J. Plus

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

The Dirac equation in (1 + 2) -dimensional Gürses space-time backgrounds

Ahmed

2019

Eur. Phys. J. Plus

View full text Add to dashboard Cite

show abstract

“…When the sum of scalar and vector potentials becomes a constant or U (r) = C p so-called the pseudospin symmetry, in this case the Dirac equation has pseudospin symmetric solutions that the pseudospin symmetry is an exact symmetry for Dirac Hamiltonian under the condition dU (r) dr = 0 in which U (r) is a constant. Now for W (r) = C s , the Dirac equation has spin symmetric solutions that the spin symmetry is an exact symmetry for Dirac Hamiltonian under the condition dW (r) dr = 0 in which W (r) is a constant [34][35][36]. Since graphene's spin plays as the role of the pseudospin, then eigenvectors of the bilayer graphene is introduced as a pseudospin.…”

Section: Massive Dirac Equationmentioning

confidence: 99%

Energy spectrum of massive Dirac particles in gapped graphene with Morse potential

Zali,

Amani,

Sadeghi

et al. 2021

Preprint

View full text Add to dashboard Cite

In this paper, we study the massive Dirac equation with the presence of the Morse potential in polar coordinate. The Dirac Hamiltonian is written as two second-order differential equations in terms of two spinor wavefunctions. Since the motion of electrons in graphene is propagated like relativistic fermionic quasi-particles, then one is considered only with pseudospin symmetry for aligned spin and unaligned spin by arbitrary k. Next, we use the confluent Heun's function for calculating the wavefunctions and the eigenvalues. Then, the corresponding energy spectrum obtains in terms of N and k. Afterward, we plot the graphs of the energy spectrum and the wavefunctions in terms of k and r, respectively. Moreover, we investigate the graphene band structure by a linear dispersion relation which creates an energy gap in the Dirac points called gapped graphene. Finally, we plot the graph of the valence and conduction bands in terms of wavevectors.

show abstract

“…Kandemir presented an analytical analysis of the two-dimensional Schrodinger equation for two interacting electrons subjected to a homogeneous magnetic field and confined by a two-dimensional external parabolic potential. Here a biconfluent Heun (BHE) equation is used [43] o Arda and Sever, in one instance with Aydogdu studied Schrodinger equation with different potentials and in two cases found Heun and confluent Heun solutions [44,45].…”

Section: Some Examples Of the Heun Equation In Physical Applicationsmentioning

confidence: 99%

Heun Functions and Some of Their Applications in Physics

Hortaçsu

2018

Advances in High Energy Physics

102

View full text Add to dashboard Cite

Most of the theoretical physics known today is described by using a small number of differential equations. For linear systems, different forms of the hypergeometric or the confluent hypergeometric equations often suffice to describe the system studied. These equations have power series solutions with simple relations between consecutive coefficients and/ or can be represented in terms of simple integral transforms. If the problem is nonlinear, one often uses one form of the Painlevé equations. There are important examples, however, where one has to use higher order equations. Heun equation is one of these examples, which recently is often encountered in problems in general relativity and astrophysics. Its special and confluent forms take names as Mathieu, Lamé and Coulomb spheroidal equations. For these equations whenever a power series solution is written, instead of a two way recursion relation between the coefficients in the series, we find one between three or four different ones. An integral transform solution using simpler functions also is not obtainable.The use of this equation in physics and mathematical literature exploded in the later years, more than doubling the number of papers with these solutions in the last decade, compared to time period since this equation was introduced in 1889 up to 2008. We use SCI data to conclude this statement, which is not precise, but in the correct ballpark. Here this equation will be introduced and examples for its use, especially in general relativity literature will be given. * This paper is a revised and many times updated version of the conference talk by the same author, published in

show abstract

Approximate Solutions of Dirac Equation with Hyperbolic-Type Potential

Cited by 8 publications

References 32 publications

The Dirac equation in (1 + 2) -dimensional Gürses space-time backgrounds

The Dirac equation in (1 + 2) -dimensional Gürses space-time backgrounds

Energy spectrum of massive Dirac particles in gapped graphene with Morse potential

Heun Functions and Some of Their Applications in Physics

Contact Info

Product

Resources

About