Asimptotik İterasyon Metodu İle Bir Dış Elektromanyetik Alan İçerisindeki Skaler Parçacıkların Hareketinin İncelenmesi

Year 2020, Volume: 10 Issue: 4, 853 - 868, 15.10.2020

Hasan Fatih Kışoğlu Kenan Söğüt

https://doi.org/10.17714/gumusfenbil.663620

Cited By: 1

Abstract

Bu çalışmada, uzay-bağımlı elektrik ve manyetik
alanların varlığında, spinsiz parçacıkların enerji özdeğerleri ve dalga
fonksiyonları incelenmektedir. Çalışmada, dış alanların iki farklı yönelimi
için Schrödinger ve Klein-Gordon denklemleri Asimptotik İterasyon Metodu (AIM)
ile çözülmektedir. Elde edilen sonuçlar, Schrödinger ve Klein-Gordon
denklemlerinin enerji özdeğerleri karşılaştırılarak göreceli katkıları
görebilmek için, ilk birkaç kuantum seviyesi için, sayısal olarak tartışılmıştır.
Alanların paralel ve ortogonal yönelimlerinde ortaya çıkan denklemlerin kuantum
koşullarını göz önüne alarak, enerji seviyelerinin eğrisi elde edilmiştir.

Keywords

Asimptotik İterasyon Metodu, Dış Alanlar, Klein-Gordon Denklemi, Schrödinger Denklemi, Skaler Parçacıklar

Investigation of the Motion of Scalar Particles in an External Electromagnetic Field via Asymptotic Iteration Method

Abstract

In the
present article, we study the energy eigenvalues and wavefuntions of the
spinless particles in the existance of space-dependent electric and magnetic
fields. The investigation is performed for two different orientations of the
external fields by solving the Schrödinger and Klein-Gordon equations via
Asymptotic Iteration Method (AIM). The obtained results are discussed
numerically for first few quantum levels to understand the relativistic
contributions by comparing the energy eigenvalues of Schrödinger and
Klein-Gordon equations. By considering the quantum conditions for the resulting
equations in the case of parallel and orthogonal orientations of the fields, we
obtained the plots for the energy levels.

Keywords

Asymptotic Iteration Method, External Fields, Klein-Gordon Equation, Schrödinger Equation, Spinless Particles

References

• Alsadi, K.S., 2015. Exact Solutions of Dirac-Rosen-Morse Problem via Asymptotic Iteration Method. Journal of Nanoelectronics and Optoelectronics, 10, 683-687.
• Aygun, M., Bayrak, O. and Bostosun, I., 2007. Solution of the radial Schrödinger equation for the potential family using the asymptotic iteration method. Journal of Physics B: Atomic, Molecular and Optical Physics, 40, 537-544.
• Bayrak, O. and Boztosun, I., 2006. Arbitrary ℓ-state solutions of the rotating Morse potential by the asymptotic iteration method. Journal of Physics A: Mathematical and General, 39, 6955-6964.
• Bayrak, O., Boztosun, I. and Ciftci, H., 2007. Exact analytical solutions to the Kratzer potential by the asymptotic iteration method. International Journal of Quantum Chemistry, 107, 540-544.
• Benchiheub, N., Kasri, Y. and Kahoul, A., 2015. Unified and simple derivation of energy levels for the Pöschl-Teller-type and Scarf-type potentials. Canadian Journal of Physics, 93, 1486-1489.
• Bergou, J. and Ehlotzky, F., 1983. Relativistic quantum states of a particle in an electromagnetic plane wave and a homogeneous magnetic field. Physical Review A, 27, 2291-2296.
• Chabab, M., El Batoul, A. and Oulne, M., 2016. Closed Analytical Solutions of the D-Dimensional Schrödinger Equation with Deformed Woods-Saxon Potential Plus Double Ring-Shaped Potential. Zeitschrift für Naturforschung A, 71, 59-68.
• Chiang, C.M. and Ho, C.L., 2001. Charged particles in external fields as physical examples of quasi-exactly-solvable models: A unified treatment. Physical Review A , 63, 062105.
• Chiu, H.Y., Canuto, V. and Fassio-Canuto, L., 1969. Nature of Radio and Optical Emissions from Pulsars. Nature, 221, 529-531.
• Chiu, H.Y. and Canuto, V., 1969. Radio Emission From Magnetic Neutron Stars. A Possible Model for Pulsars. Physical Review Letters, 22, 415.
• Chiu, H.Y. and Occhionero, F., 1969. Unified Model for Pulsars. Nature, 223, 1113-1116.
• Ciftci, H., Hall, R.L. and Saad, N., 2003. Asymptotic iteration method for eigenvalue problems. Journal of Physics A: Mathematical and General, 36, 11807-11816.
• Ciftci, H., Hall, R.L. and Saad, N., 2005a. Construction of exact solutions to eigenvalue problems by the asymptotic iteration method. Journal of Physics A: Mathematical and General, 38, 1147-1156.
• Ciftci, H., Hall, R.L. and Saad, N., 2005b. Perturbation theory in a framework of iteration methods. Physics Letters A, 340, 388-396.
• Ciftci, H., Hall, R.L. and Saad, N., 2013. Exact and approximate solutions of Schrödinger’s equation for a class of trigonometric potentials. Central European Journal of Physics, 11, 37-48.
• Ciftci, H. and Kisoglu, H.F., 2016. Application of asymptotic iteration method to a deformed well problem. Chinese Physics B, 25, 030201.
• Demić, A., Milanović, V., Radovanović, J. and Musić, M., 2016. WKB method for potentials unbounded from below, Modern Physics Letters B, 30, 1650003.
• Dong, S. H., 2007. Factorization Method in Quantum Mechanics, Springer, The Netherlands, 35p.
• Greiner, W., 1997. Relativistic Quantum Mechanics, Springer, Berlin, 41p.
• Greiner, W., 2001. Quantum Mechanics: An Introduction, Springer, Berlin, 206p.
• Grewing, M. and Heintzmann, H., 1972. Charged particle motion in superstrong electromagnetic fields. Physics Letters A, 42, 325-326.
• Griffiths, D. J., 1991. Introduction to Electrodynamics, Prentice-Hall International, Inc., U.S.A, 347p.
• Ivanovski, G., Jakimovski, D. and Sopova, V., 1993. Energy levels of a charged particle in a homogeneous electric field orthogonal to a piecewise homogeneous magnetic field. Physics Letters A, 183, 24-28.
• Kumaresan, N., Kamali, M.Z.M. and Ratnavelu, K., 2015. Solution of the Fuzzy Schrödinger Equation in Positron-Hydrogen Scattering Using Ant Colony Programming. Chinese Journal of Physics, 53, 080401.
• Lam, L., 1971. Motion in Electric and Magnetic Fields. I. Klein-Gordon Particles. Journal of Mathematical Physics, 12, 299-303.
• Liboff, R.L., 1966. Brownian Motion of Charged Particles in Crossed Electric and Magnetic Fields. Physical Review, 141, 222-227.
• Nikiforov, A. F. and Uvarov, U. V., 1988. Special Functions of Mathematical Physics, Birkhauser Verlag, Basel, 1p.
• Occhionero, F. and Demianski, M., 1969. Electric Fields in Rotating, Magnetic, Relativistic Stars. Physical Review Letters., 23, 1128-1130.
• Onate, C.A. and Idiodi, J.O.A., 2015. Eigensolutions of the Schrödinger Equation with Some Physical Potentials. Chinese Journal of Physics, 53, 120001.
• Redmond, P.J., 1965. Solution of the Klein-Gordon and Dirac Equations for a Particle with a Plane Electromagnetic Wave and a Parallel Magnetic Field. Journal of Mathematical Physics, 6, 1163-1169.
• Rutkowski, A. and Poszwa, A., 2009. Relativistic corrections for a two-dimensional hydrogen-like atom in the presence of a constant magnetic field. Physica Scripta, 79, 065010.
• Sogut, K. and Havare, A., 2014. Spinless Particles in Exponentially Varying Electric and Magnetic Fields. Advances in High Energy Physics, 2014, 493120.
• Sogut, K. and Havare, A., 2015. On the scalar particle creation by electromagnetic fields in Robertson–Walker spacetime. Nuclear Physics B, 901, 76-84.
• Valance, A., Morgan, T.J. and Bergeron, H., 1990. Eigensolution of the Coulomb Hamiltonian via supersymmetry. American Journal of Physics, 58, 487-491.
• Villalba, V.M. and Pino, R., 2001. Energy spectrum of a relativistic two-dimensional hydrogen-like atom in a constant magnetic field of arbitrary strength. Physica E, 10, 561-568.
• Zhang, C.Y., Zhang, S.J. and Wang, B., 2015. Charged scalar perturbations around Garfinkle-Horowitz-Strominger black holes. Nuclear Physics B, 899, 37-54.