EFFECTIVE MASS KLEIN-GORDON EQUATION WITH POSITION DEPENDENT MAGNETIC FIELD

Year 2019, Volume: 2 Issue: 1, 32 - 35, 30.01.2019

Özgür Mızrak , Oktay Aydoğdu , Kenan Söğüt

https://doi.org/10.33773/jum.506496

Cited By: 3

Abstract

Recently, exact solutions of the classical and relativistic wave equations for the existance of an external potential have been widely studied in view of the position-dependent mass formalism. Such eorts have important applications in technology, especially in material science such as electronic properties of the semi-conductors and quantum dots. In the present study, we aim to obtain exact solutions of the Klein-Gordon equation in the presence of an exponential magnetic eld via effective mass formalism. Energy eigenvalues are derived by using wave functions. The studied magnetic eld and effective mass have the form ~B = B0e􀀀x^k and m(x) = (m0 + m1e􀀀x).

Keywords

Klein-Gordon equations, external elds

References

• P. J. Redmond, Solution of the Klein-Gordon and Dirac equations for a particle with a plane electromagnetic wave and a parallel magnetic _eld, Journal of Mathematical Physics, vol. 6, pp. 11631169, (1965).L. Lam, Motion in electric and magnetic _elds. I. Klein-Gordon particles, Journal of Mathematical Physics, vol. 12, no.2, pp. 299303, (1971). G. Ivanovski, D. Jakimovski, and V. Sopova, Energy levels of a charged particle in a homogeneous electric _eld orthogonal to a piecewise homogeneous magnetic _eld, Physics Letters A, vol. 183, no. 1, pp. 2428, (1993). V. M. Villalba and R. Pino, Energy spectrum of a relativistic two-dimensional hydrogen-like atom in a constant magnetic _eld of arbitrary strength, Physica E: Low-Dimensional Systems and Nanostructures, vol. 10, no. 4, pp. 561568, (2001).K. Sogut, H. Yanar, A. Havare, "Production of Dirac Particles in External Electromagnetic Fields", Acta Physica Polonica B, No 9, Vol. 48, (2017).L. Dekar, L. Chetouani and T. F. Hamann,"Wave function for smooth potential and mass step", Physical Review A 59, 107, (1999).A. S. Dutra and C. A. S. Almeida, "Exact solvability of potentials with spatially dependent e_ective masses", Physics Letters A 275, 25, (2000).R. Koc, M. Koca and E. Korcuk, "A new class of quasi-exactly solvable potentials with a position-dependent mass", Journal Physics A, 35, L527, (2002).B. Gonul, O. Ozer, B. Gonul B and F. Uzgun, "Exact Solutions of E_ective-Mass Schrodinger Equations" Modern Physics Letters A, 17, 2453, (2002).C. Tezcan and R. Sever, "Exact Solutions of the Schrodinger Equation with Positiondependent E_ective Mass via General Point Canonical Transformation", Journal of Mathematical Chemistry, 42, 387,(2007).R. Sever and C. Tezcan, "Exact Solution of the Schrodinger Equation for the ModifiedKratzer's Molecular Potential With Position-Dependent Mass" International Journal of Modern Physics E, 17, 1327, (2008).A. D. Alhaidari, "Solution of the Dirac equation with position-dependent mass in the Coulomb _eld", Physics Letters A, 322, 12, (2004).O. Mustafa and S. H. Mazharimousavi, "First-Order Intertwining Operators with Position Dependent Mass and -Weak-Pseudo-Hermiticity Generators", International Journal of Theoretical Physics, 47, 446, (2008).C. S. Jia and A. S. Dutra, "Extension of PT-symmetric quantum mechanics to the Dirac theory with position-dependent mass", Annals of Physics, 323, 566, (2008).A. Arda, R. Sever, C. Tezcan, "Analytical Solutions to the KleinGordon Equation with Position-Dependent Mass for q-Parameter Poschl-Teller Potential", Chinese Physics Letters Vol. 27, No. 1, 010306, (2010).O. Aydogdu, A. Arda and R. Sever, "Scattering of a spinless particle by an asymmetric Hulthn potential within the e_ective mass formalism", Journal of Mathematical Physics 53, 102111, (2012).M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, Dover, New York, NY,USA, (1970).K. Handrich, "Quantum mechanical magnetic-_eld-gradient drift velocity:An analytically solvable model", Physical Review B, 72, 161308(R), (2005).