Analytical solution of D-dimensional radial Schrödinger equation for sextic potential by the extended Nikiforov–Uvarov method and biconfluent Heun polynomials
Yıl: 2019 Cilt: 43 Sayı: 4 Sayfa Aralığı: 410 - 416 Metin Dili: İngilizce DOI: 10.3906/fiz-1904-28 İndeks Tarihi: 12-05-2020
Analytical solution of D-dimensional radial Schrödinger equation for sextic potential by the extended Nikiforov–Uvarov method and biconfluent Heun polynomials
Öz: D-dimensional radial Schrödinger equation (SE) for sextic potential is solved using the extended Nikiforov–Uvarov method analytically. Energy eigenvalue and eigenfunction solutions are achieved systematically. It is alsopresented that the D-dimensional radial SE is transformed to biconfluent Heun equation (BHE). Therefore the eigenfunctionsolutions for the potential are attained in terms of biconfluent Heun polynomials when the condition of existenceof polynomial solution of BHE is provided simultaneously.
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- [1] Znojil M. Exact solution for Morse oscillator in PT-symmetric quantum mechanics. Physics Letters A 1999; 264 (1-2): 108-111. doi:10.1016/S0375-9601(99)00805-1
- [2] Eğrifes H, Demirhan D, Büyükkılıç F. Exact solutions of the Schrödinger equation for two “deformed” hyperbolic molecular potentials. Physica Scripta 1999a; 60 (3): 195-198. doi:10.1238/Physica.Regular.060a00195
- [3] Eğrifes H, Demirhan D, Büyükkılıç F. Polynomial solutions of the Schrödinger equation for the ”deformed” hyperbolic potentials by Nikiforov-Uvarov method. Physica Scripta 1999b; 59 (2): 90-94. doi:10.1238/Physica.Regular.059a00090
- [4] Eğrifes H, Sever R. Bound states of the Dirac equation for the PT-symmetric generalized Hulthen potential by the Nikiforov-Uvarov method. Physics Letters A 2005; 344 (2-4), 117-126. doi:10.1016/j.physleta.2005.06.061
- [5] Şimşek M, Eğrifes H. The Klein–Gordon equation of generalized Hulthen´ potential in complex quantum mechanics. Journal of Physics A: Mathematical and General 2004; 37 (15): 4379-4393. doi:10.1088/0305-4470/37/15/007
- [6] Yasuk F, Berkdemir C, Berkdemir A, Önem C. Exact solutions of the Duffin-Kemmer-Petiau equation for the deformed Hulthen potential. Physica Scripta 2005; 71 (4): 340-343. doi:10.1238/physica.regular.071a00340
- [7] Sever R, Tezcan C, Aktaş M, Yeşiltaş Ö. Exact solution of Schrödinger equation for Pseudoharmonic potential. Journal of Mathematical Chemistry 2008; 43 (2): 845-851. doi:10.1007/s10910-007-9233-y
- [8] Aktaş M. Exact bound state solutions of the Schrödinger equation for noncentral potential via the Nikiforov-Uvarov method. International Journal of Theoretical Physics 2009; 48 (7): 2154-2163. doi:10.1007/s10773-009-9993-1
- [9] Ishkhanyan AM. Exact solution of the Schrödinger equation for a short-range exponential potential with inverse square root singularity. European Physical Journal Plus 2018; 133 (3): 83-90. doi:10.1140/epjp/i2018-11912-5 [10] Dong SH. Wave Equations in Higher Dimensions. New York, NY, USA: Springer Netherlands, 2011.
- [11] Hassanabadi H, Zarrinkamar S, Rajabi1 AA. Exact solutions of D-dimensional Schroedinger equation for an energy-dependent potential by NU method. Communications in Theoretical Physics 2011; 55 (4): 541-544. doi:10.1088/0253-6102/55/4/01
- [12] Assi IA, Ikot AN, Chukwuocha EO. Solutions of the D-Dimensional Schrödinger Equation with the Hyperbolic Pöschl-Teller Potential plus Modified Ring-Shaped Term. Advances in High Energy Physics 2018; 2018: 1-9. doi:10.1155/2018/4536543
- [13] Dong SH, Sun GH, Popov D. Group theory approach to the Dirac equation with a Coulomb plus scalar potential in D+1 dimensions. Journal of Mathematical Physics 2003; 44 (10): 4467-4479. doi:10.1063/1.1604185
- [14] Oyewumi KJ, Akinpelu FO, Agboola AD. Exactly complete solutions of the pseudoharmonic potential in Ndimensions. International Journal of Theoretical Physics 2008; 47 (4): 1039-1057. doi:10.1007/s10773-007-9532-x
- [15] Ibrahim TT, Oyewumi KJ, Wyngaardt SM. Analytical solution of N-dimensional Klein-Gordon and Dirac equations with Rosen-Morse potential. European Physical Journal Plus 2012; 127 (9): 100-109. doi:10.1140/epjp/i2012-12100- 5
- [16] Karayer H, Demirhan D, Büyükkılıç F. Extension of Nikiforov-Uvarov method for the solution of Heun equation. Journal of Mathematical Physics 2015; 56 (6): 063504. doi:10.1063/1.4922601
- [17] Nikiforov AV, Uvarov VB. Special Functions of Mathematical Physics. Boston, MA, USA: Birkhauser Basel, 1988.
- [18] Karayer H, Demirhan D, Büyükkılıç F. Some special solutions of biconfluent and triconfluent Heun equations in elementary functions by extended Nikiforov–Uvarov method. Reports on Mathematical Physics 2015; 76 (3): 271-281. doi:10.1016/S0034-4877(15)00039-7
- [19] Karayer H, Demirhan D, Büyükkılıç F. Solution of Schrödinger equation for two different potentials using extended Nikiforov-Uvarov method and polynomial solutions of biconfluent Heun equation. Journal of Mathematical Physics 2018; 59 (5): 053501. doi:10.1063/1.5022008
- [20] Pahlavani MR. Theoretical Concepts of Quantum Mechanics. Rijeka, Croatia: InTech, 2012.
- [21] Ronveaux A. Heun’s Differential Equations. New York, NY, USA: Springer, 1995.
- [22] Ferreira EM, Sesma J. Global solutions of the biconfluent Heun equation. Numerical Algorithms 2016; 71 (4): 797-809. doi:10.1007/s11075-015-0024-4
| APA | KARAYER H (2019). Analytical solution of D-dimensional radial Schrödinger equation for sextic potential by the extended Nikiforov–Uvarov method and biconfluent Heun polynomials. , 410 - 416. 10.3906/fiz-1904-28 |
| Chicago | KARAYER HASİBE HALE Analytical solution of D-dimensional radial Schrödinger equation for sextic potential by the extended Nikiforov–Uvarov method and biconfluent Heun polynomials. (2019): 410 - 416. 10.3906/fiz-1904-28 |
| MLA | KARAYER HASİBE HALE Analytical solution of D-dimensional radial Schrödinger equation for sextic potential by the extended Nikiforov–Uvarov method and biconfluent Heun polynomials. , 2019, ss.410 - 416. 10.3906/fiz-1904-28 |
| AMA | KARAYER H Analytical solution of D-dimensional radial Schrödinger equation for sextic potential by the extended Nikiforov–Uvarov method and biconfluent Heun polynomials. . 2019; 410 - 416. 10.3906/fiz-1904-28 |
| Vancouver | KARAYER H Analytical solution of D-dimensional radial Schrödinger equation for sextic potential by the extended Nikiforov–Uvarov method and biconfluent Heun polynomials. . 2019; 410 - 416. 10.3906/fiz-1904-28 |
| IEEE | KARAYER H "Analytical solution of D-dimensional radial Schrödinger equation for sextic potential by the extended Nikiforov–Uvarov method and biconfluent Heun polynomials." , ss.410 - 416, 2019. 10.3906/fiz-1904-28 |
| ISNAD | KARAYER, HASİBE HALE. "Analytical solution of D-dimensional radial Schrödinger equation for sextic potential by the extended Nikiforov–Uvarov method and biconfluent Heun polynomials". (2019), 410-416. https://doi.org/10.3906/fiz-1904-28 |
| APA | KARAYER H (2019). Analytical solution of D-dimensional radial Schrödinger equation for sextic potential by the extended Nikiforov–Uvarov method and biconfluent Heun polynomials. Turkish Journal of Physics, 43(4), 410 - 416. 10.3906/fiz-1904-28 |
| Chicago | KARAYER HASİBE HALE Analytical solution of D-dimensional radial Schrödinger equation for sextic potential by the extended Nikiforov–Uvarov method and biconfluent Heun polynomials. Turkish Journal of Physics 43, no.4 (2019): 410 - 416. 10.3906/fiz-1904-28 |
| MLA | KARAYER HASİBE HALE Analytical solution of D-dimensional radial Schrödinger equation for sextic potential by the extended Nikiforov–Uvarov method and biconfluent Heun polynomials. Turkish Journal of Physics, vol.43, no.4, 2019, ss.410 - 416. 10.3906/fiz-1904-28 |
| AMA | KARAYER H Analytical solution of D-dimensional radial Schrödinger equation for sextic potential by the extended Nikiforov–Uvarov method and biconfluent Heun polynomials. Turkish Journal of Physics. 2019; 43(4): 410 - 416. 10.3906/fiz-1904-28 |
| Vancouver | KARAYER H Analytical solution of D-dimensional radial Schrödinger equation for sextic potential by the extended Nikiforov–Uvarov method and biconfluent Heun polynomials. Turkish Journal of Physics. 2019; 43(4): 410 - 416. 10.3906/fiz-1904-28 |
| IEEE | KARAYER H "Analytical solution of D-dimensional radial Schrödinger equation for sextic potential by the extended Nikiforov–Uvarov method and biconfluent Heun polynomials." Turkish Journal of Physics, 43, ss.410 - 416, 2019. 10.3906/fiz-1904-28 |
| ISNAD | KARAYER, HASİBE HALE. "Analytical solution of D-dimensional radial Schrödinger equation for sextic potential by the extended Nikiforov–Uvarov method and biconfluent Heun polynomials". Turkish Journal of Physics 43/4 (2019), 410-416. https://doi.org/10.3906/fiz-1904-28 |
