An improvement of the asymptotic iteration method for exactly solvable eigenvalue problems

被引:19
作者
Boztosun, I. [1 ]
Karakoc, M. [1 ]
机构
[1] Erciyes Univ, Dept Phys, Fac Arts & Sci, Kayseri, Turkey
关键词
D O I
10.1088/0256-307X/24/11/004
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
We derive a formula that simplifies the original asymptotic iteration method formulation to find the energy eigenvalues for the analytically solvable cases. We then show that there is a connection between the asymptotic iteration and the Nikiforov-Uvarov methods, which both solve the second order linear ordinary differential equations analytically.
引用
收藏
页码:3028 / 3031
页数:4
相关论文
共 50 条
[21]   CLASSIFICATION OF EXACTLY SOLVABLE POTENTIAL PROBLEMS [J].
BEKER, H .
FOUNDATIONS OF PHYSICS, 1993, 23 (05) :851-856
[22]   ITERATION IN SEMIDEFINITE EIGENVALUE PROBLEMS [J].
DEVEUBEKE, BMF .
JOURNAL OF THE AERONAUTICAL SCIENCES, 1955, 22 (10) :710-720
[23]   ITERATION IN SEMIDEFINITE EIGENVALUE PROBLEMS [J].
PINES, S .
JOURNAL OF THE AERONAUTICAL SCIENCES, 1956, 23 (04) :380-381
[24]   ITERATION METHODS IN EIGENVALUE PROBLEMS [J].
DYAKONOV, EG .
MATHEMATICAL NOTES, 1983, 34 (5-6) :945-953
[25]   AN EFFECTIVE ESTIMATE OF THE CONVERGENCE OF AN IMPLICIT ITERATION METHOD FOR EIGENVALUE PROBLEMS [J].
ZHUK, PF ;
PRIKAZCHIKOV, VG .
DIFFERENTIAL EQUATIONS, 1982, 18 (07) :837-841
[26]   Multigrid Method for Nonlinear Eigenvalue Problems Based on Newton Iteration [J].
Xu, Fei ;
Xie, Manting ;
Yue, Meiling .
JOURNAL OF SCIENTIFIC COMPUTING, 2023, 94 (02)
[27]   A Jacobi-Davidson iteration method for linear eigenvalue problems [J].
Sleijpen, GLG ;
VanderVorst, HA .
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 1996, 17 (02) :401-425
[28]   A Jacobi-Davidson iteration method for linear eigenvalue problems [J].
Sleijpen, GLG ;
Van der Vorst, HA .
SIAM REVIEW, 2000, 42 (02) :267-293
[29]   Multigrid Method for Nonlinear Eigenvalue Problems Based on Newton Iteration [J].
Fei Xu ;
Manting Xie ;
Meiling Yue .
Journal of Scientific Computing, 2023, 94
[30]   QUANTUM-MECHANICS - PROBLEMS INTERMEDIATE WITH RESPECT TO EXACTLY SOLVABLE AND EXACTLY NONSOLVABLE PROBLEMS [J].
TURBINER, AV .
ZHURNAL EKSPERIMENTALNOI I TEORETICHESKOI FIZIKI, 1988, 94 (02) :33-44