[1]
|
L. I. Schiff, “Quantum Mechanics,” 3rd Edition, McGraw-Hill, New York, 1955.
|
[2]
|
L. D. Landau and E. M. Lifshitz, “Quantum Mechanics, Non-Relativistic Theory,” 3rd. Edition, Pergamon, Oxford, 1977.
|
[3]
|
C. L. Pekeris, “The Rota-tion-Vibration Coupling in Diatomic Molecules,” Physical Review, Vol. 45, 1934, pp. 98-103. doi:10.1103/PhysRev.45.98
|
[4]
|
O. Bayrak and I. Boztosun, “Arbitrary -State Solutions of the Rotating Morse Potential by the Asymptotic Iteration Method,” Journal of Physics A: Mathematical and General, Vol. 39, No. 22, 2006, pp. 6955-6964.
doi:10.1088/0305-4470/39/22/010
|
[5]
|
W.C. Qiang and S. H. Dong, “Arbitrary l-State Solutionsof the Rotating Morse poten-tial Through the Exact Quantization Method,” Physics Letters A, Vol. 363, No.3, 2007, pp. 169-176.
doi:10.1016/j.physleta.2006.10.091
|
[6]
|
S. M. Ikhdair, “An Approximate State Solutions of the Dirac Equation for the Generalized Morse Potential under Spin and Pseudospin Symmetry,” Journal of Mathematical Physics, Vol. 52, No. 5, 2011, pp. 052303- 052322. doi:10.1063/1.3583553
|
[7]
|
S. M. Ikh-dair and R. Sever, “Any -State Solutions of the Woods-Saxon Potential in Arbitrary Dimension within the New Improved Quantization Rule,” International Journal of Modern Physics A, Vol. 25, No. 20, 2010, pp. 3941-3952. doi:10.1142/S0217751X10050160
|
[8]
|
S. M. Ikhdair and R. Sever, “Exact Solution of the Klein-Gordon Equation for the PT-Symmetric Generalized Woods-Saxon Potential by the Nikiforov-Uvarov Method,” Annals of Physics (Leibzig), Vol. 16, No. 3, 2007, pp. 218-232. doi:10.1002/andp.200610232
|
[9]
|
S. M. Ikhdair and R. Sever, “Approximate Eigenvalue and Eigen Function Solutions for the Generalized Hulthén Potential with any Angular Momentum,” Journal of Mathematical Chemistry, Vol. 42, No. 3, 2007, pp. 461- 471. doi:10.1007/s10910-006-9115-8
|
[10]
|
C. Y. Chen, D. S. Sun and F. L. Lu, “Approximate Analytical Solutions of Klein-Gordon Equation with Hulthén Potentials for Nonzero Angular Momentum,” Physics Letters A, Vol. 370, No. 3-4, 2007, pp. 219-221;
doi:10.1016/j.physleta.2007.05.079
|
[11]
|
W. C. Qiang, R. S. Zhou and Y. Gao, “Any -State Solutions of the Klein-Gordon with the Generalized Hulthén Potential,” Physics Letters A, Vol. 371, No. 3, 2007, pp. 201-204; doi:10.1016/j.physleta.2007.04.109
|
[12]
|
S. Dong, S.-H. Dong, H. Bahlouli and V. B. Bezzerra, “Algebraic Approach to the Klein-Gordon Equation with Hyperbolic Scarf Potential,” In-ternational Journal of Modern Physics E, Vol. 20, No.1, 2011, pp. 55-61.
doi:10.1142/S0218301311017326
|
[13]
|
S. M. Ikhdair and J. Abu-Hasna, “Quantization Rule Solution to the Hulthén Poten-tial in Arbitrary Dimension with a New Approximate Scheme for the Centrifugal Term,” Physica Scripta, Vol. 83, No.2, 2011, pp. 025002-7. doi:10.1088/0031-8949/83/02/025002
|
[14]
|
G.-F. Wei, Z.-Z. Zhen and S.-H. Dong, “The Relativistic Bound and Scattering States of the Manning-Rosen Potential with an Improved New Approximate Scheme to the Centrifugal Term,” Central European Journal of Physics, Vol. 7, No. 1, 2009, pp. 175-183.
doi:10.2478/s11534-008-0143-9
|
[15]
|
S.M. Ikhdair and R. Sever, “Approximate Bound State Solutions of Dirac Equation with Hulthén Potential Including Coulomb-Like Tensor Poten-tial,” Applied Mathe- matics and Computation, Vol. 216, No. 3, 2010, pp. 911- 923. doi:10.1016/j.amc.2010.01.104
|
[16]
|
S. Flügge, “Practical Quantum Mechanics,” Vol. 1, Springer, Berlin, 1994.
|
[17]
|
J. Y. Guo, J. Meng and F. X. Xu, “Any -State Solutions of the Klein-Gordon Equation with Special Hulthén Potentials,” Chiniese Physics Letters, Vol. 20, 2003, pp. 602-604.
|
[18]
|
A. D. Alhaidari, “Solution of the Relativistic Dirac-Hulthen Problem,” Journal of Physics A, Vol. 37, 2004, pp. 5805-5813. doi:10.1088/0305-4470/37/22/007
|
[19]
|
O. Bayrak, G. Kocak and I. Boztosun, “Any -State Solutions of the Hulthén Potential by the Asymptotic Iteration Method,” Journal of Physics A: Mathematical and General, Vol. 39, 2006, pp. 11521-11529.
doi:10.1088/0305-4470/39/37/012
|
[20]
|
S. Haouat and L. Che-touani, “Approximate Solutions of Klein-Gordon and Dirac Equations in the Presence of the Hulthén Potential,” Physica Scripta, Vol. 77, 2008, pp. 025005-6; doi:10.1088/0031-8949/77/02/025005
|
[21]
|
E. Ol?ar, R. Ko? and H. Tütüncüler, “The Exact Solution of the s-Wave Klein-Gordon Equation for the Generalized Hulthén Potential by the Asymptotic Iteration Method,” Physica Scripta, Vol. 78, 2008, pp. 015011-4;
|
[22]
|
C. S. Jia, J. Y. Liu and P. Q. Wang, “A New Approximation Scheme for the Centrifugal Term and Hulthén Potential,” Physics Letters A, Vol. 372, 2008, pp. 4779-4782.
|
[23]
|
S.-H. Dong, “A New Quantization Rule to the Energy Spectra for Modified Hyperbolic-Type Potentials,” International Journal of Quantum Chemistry, Vol. 109, No. 4, 2009, pp. 701-707. doi:10.1002/qua.21862
|
[24]
|
M. F. Man-ning, “Exact Solutions of the Schr?dinger Equation,” Physical Review, Vol. 48, 1935, pp. 161-164.
doi:10.1103/PhysRev.48.161
|
[25]
|
A. Diaf, A. Chouchaoui and R. L. Lombard, “Feynman Integral Treatment of the Bargmann Potential,” Annals of Physics, Vol. 317, 2005, pp. 354-365.
doi:10.1016/j.aop.2004.11.010
|
[26]
|
G.-F. Wei, C.-Y. Long and S.-H. Dong, “The Scattering of the Manning- Rosen Potential with Centrifugal Term,” Physics Letters A, Vol. 372, No. 15, 2008, pp. 2592-2596.
doi:10.1016/j.physleta.2007.12.042
|
[27]
|
S.-H. Dong and J. Garcia-Ravelo, “Exact Solutions of the s-Wave Schr?dinger Equation with Manning-Rosen Potential,” Physica Scripta, Vol. 75, 2007, pp. 307-309.
doi:10.1088/0031-8949/75/3/013
|
[28]
|
W.-C. Qiang and S. H. Dong, “Analytical Approximation to the Solutions of the Manning-Rosen Potential with Centrifugal Term,” Physics Letters A, Vol. 368, No.1-2, 2007, pp. 13-17. doi:10.1016/j.physleta.2007.03.057
|
[29]
|
W.-C. Qiang and S.-H. Dong, “The Manning-Rosen Potential Studied by a New Approximate Scheme to the Centrifugal Term,” Physica Scripta, Vol. 79, No. 4, 2009, p. 045004. doi:10.1088/0031-8949/79/04/045004
|
[30]
|
C. Y. Chen, F. L. Lu and D. S. Sun, “Exact Solutions of Scattering States for the s-Wave Schr?dinger Equation with the Manning-Rosen Poten-tial,” Physica Scripta, Vol. 76, 2007, pp. 428-430. doi:10.1088/0031-8949/76/5/003
|
[31]
|
S. M. Ikhdair, “On the Bound-State Solutions of the Manning-Rosen Potential Includ-ing an Improved Approximation to the Orbital Centrifugal Term,” Physica Scripta, Vol. 83, 2011, pp. 015010-10.
doi:10.1088/0031-8949/83/01/015010
|
[32]
|
E. Ol?ar, R. Ko? and H. Tütüncüler, “Bound States of the s-Wave Equation with Equal Scalar and Vector Standard Eckart Potential,” Chinese Physics Letters, Vol. 23, 2006, pp. 539-541. doi:10.1088/0256-307X/23/3/004
|
[33]
|
W.-C. Qiang, J.-Y. Wu and S.-H. Dong, “The Eckart- Like Potential Studied by a New Approximate Scheme to the Centrifugal Term,” Physica Scripta, Vol. 79, No. 6, 2009, p. 065011. doi:10.1088/0031-8949/79/06/065011
|
[34]
|
X. Zou, L. Z. Yi and C. S. Jia, “Bound States of the Dirac Equation with Vector and Scalar Eckart Potentials,” Physics Letters A, Vol. 346, 2005, pp. 54-64.
doi:10.1016/j.physleta.2005.07.075
|
[35]
|
G.-F. Wei, S.-H. Dong and V. B. Bezerra, “The Relativistic Bound and Scatter-ing States of the Eckart Potential with a Proper New Approxi-mate Scheme for the Centrifugal Term,” International Journal of Modern Physics A, Vol. 24, No. 1, 2009, pp. 161-172.
doi:10.1142/S0217751X09042621
|
[36]
|
C. S. Jia, P. Guo and X. L. Peng, “Exact Solutions of the Dirac-Eckart Problem with Spin and Pseudospin Symmetry,” Journal of Physics A: Mathematical and Theoretical, Vol. 39, No. 24, 2006, pp. 7737-7744.
doi:10.1088/0305-4470/39/24/010
|
[37]
|
S. H. Dong, W. C. Qiang, G. H. Sun and V. B. Bezerra, “Analytical Approxima-tions to the -Wave Solutions of the Schr?dinger Equation with the Eckart Potential,” Journal of Physics A: Mathematical and Theoretical, Vol. 40, No. 34, 2007, pp. 10535-10540.
doi:10.1088/1751-8113/40/34/010
|
[38]
|
W.-C. Qiang and S.-H. Dong, “Analytical Approximation to the -Wave Solutions of the Klein-Gordon Equation for a Second P?schl-Teller Like Potential,” Physics Letters A, Vol. 372, No. 27-28, 2008, pp. 4789-4792.
doi:10.1016/j.physleta.2008.05.020
|
[39]
|
S. M. Ikhdair, “Ap-proximate Solutions of the Dirac Equation for the Rosen-Morse Potential Including the Spin-Orbit Centrifugal Term,” Journal of Mathematical Physics, Vol. 51, No. 2, 2010, pp. 023525-16;
doi:10.1063/1.3293759
|
[40]
|
G.-F. Wei and S.-H. Dong, “Pseudospin Symmetry for Modified Rosen-Morse Potential Including a Pekeris- Type Approximation to the Pseudo-Centrifugal Term,” The European Physical Journal A, Vol. 46, No. 2, 2010, pp. 207-212. doi:10.1140/epja/i2010-11031-0
|
[41]
|
C. Eckart, “The Penetra-tion of a Potential Barrier by Electrons,” Physics Review, Vol. 35, No. 11, 1930, pp. 1303-1309. doi:10.1103/PhysRev.35.1303
|
[42]
|
F. Cooper, A. Khare and U. Sukhatme, “Supersymmetry and Quantum Mechanics,” Physics Report, Vol. 251, No. 5-6, 1995, pp. 267-385.
doi:10.1016/0370-1573(94)00080-M
|
[43]
|
J. J. Weiss, “Mechanism of Proton Transfer in Acid-Base Reactions,” Journal of Chemical Physics, Vol. 41, 1964, pp. 1120-1124. doi:10.1063/1.1726015
|
[44]
|
A. Cimas, M. Aschi, C. Barrien-tos, V. M. Ray?n, J. A. Sordo and A. Largo, “Computational Study on the Kinetics of the Reaction of with ,” Chemical Physics Letters , Vol. 374, No. 5-6, 2003, pp. 594-600.
doi:10.1016/S0009-2614(03)00771-1
|
[45]
|
C. S. Jia, X. L. Zeng and L. T. Sun, “PT Symmetry and Shape Invariance for a Potential Well with a Barrier,” Physics Letters A, Vol. 294, No. 3-4, 2002, pp. 185-189.
doi:10.1016/S0375-9601(01)00840-4
|
[46]
|
C. S. Jia, Y. Li, Y. Sun, J. Y. Liu and L. T. Sun, “Bound States of the Five Parametric Exponential-Type Potential Model,” Physics Letters A, Vol. 311, No. 2-3, 2003, pp. 115-125. doi:10.1016/S0375-9601(03)00502-4
|
[47]
|
H. E?rifes, D. Demirhan and F. Büyükk?l??, “Exact Solutions of the Schr?dinger Equation for Two Deformed Hyperbolic Molecu-lar Potentials,” Physica Scripta, Vol. 60, No.3, 1999, pp. 195-198.
doi:10.1238/Physica.Regular.060a00195
|
[48]
|
A. Arai, “Ex-actly Solvable Supersymmetric Quantum Mechanics,” Journal of Mathematical Analysis and Applications, Vol. 158, No.1, 1991, pp. 63-79.
doi:10.1016/0022-247X(91)90267-4
|
[49]
|
R. Dutt, A. Khare and U. Sukhatme, “Supersymmetry, Shape Invariance, and Exactly Solvable Potentials,” American Journal of Physics, Vol. 56, No.2, 1988, pp. 163-168. doi:10.1119/1.15697
|
[50]
|
R. De, R. Dutt and U. Sukhatme, “Mapping of Shape Invariant Poten-tials Under Point Canonical Transformations,” Journal of Physics A: Mathematical and General, Vol. 25, No. 13, 1992, pp. L843-L850.
doi:10.1088/0305-4470/25/13/013
|
[51]
|
M. Hruska, W.Y. Ke-ung and U. Sukhatme, “Accuracy of semi classical Methods for Shape-Invariant Potentials,” Physics Review A, Vol. 55, No. 5, 1997, pp. 3345-3350.
doi:10.1103/PhysRevA.55.3345
|
[52]
|
L.Z. Yi, Y.F. Diao, J.Y. Liu and C.S. Jia, “Bound States of the Klein-Gordon Equation with Vector and Scalar Rosen-Morse-Type Potentials,” Physics Letters A, Vol. 333, 2004, pp. 212-217.
doi:10.1016/j.physleta.2004.10.054
|
[53]
|
R.L. Greene and C. Aldrich, “Variational Wave Functions for a Screened Coulomb Potential,” Physics Review A, Vol. 14, 1976, pp. 2363-2366.
doi:10.1103/PhysRevA.14.2363
|
[54]
|
G. F. Wei, C. Y. Long, X. Y. Duan and S. H. Dong, “Arbitrary -Wave Scattering State Solutions of the Schr?dinger Equation for the Eckart Potential,” Physica Scripta, Vol. 77, 2008, pp. 035001-5.
doi:10.1088/0031-8949/77/03/035001
|
[55]
|
C. Y. Chen, D. S. Sun and F.L. Lu, “Analytical Approximations of Scattering States to the -Wave Solutions for the Schr?dinger Equation with the Eckart Potential,” Journal of Physics A: Mathematical and Theoretical, Vol. 41, No. 3, 2008, pp. 035302.
doi:10.1088/1751-8113/41/3/035302
|
[56]
|
A. Soylu, O. Bayrak and I. Boztosun, “ -State Solutions of the Dirac Equation for the Eckart Potential with Pseudospin- and Spin-Symmetry,” Journal of Physics A: Mathematical and Theoretical, Vol. 41, 2008, pp. 065308-8. doi:10.1088/1751-8113/41/6/065308
|
[57]
|
L. H. Zhang, X. P. Li and C. S. Jia, “Analytical Approximation to the Solution of the Dirac Equation with the Eckart Potential Including the Spin-Orbit Coupling Term,” Physics Letters A, Vol. 372, 2008, pp. 2201-2207.
doi:10.1016/j.physleta.2007.11.022
|
[58]
|
Y. Zhang, “Approxi-mate Analytical Solutions of the Klein-Gordon Equation with scalar and Vector Eckart Potentials,” Physica Scripta, Vol. 78, 2008, pp. 015006-4.
doi:10.1088/0031-8949/78/01/015006
|
[59]
|
C. S. Jia, J. Y. Liu and P. Q. Wang, “A New Approximation Scheme for the Cen-trifugal Term and the Hulthén Potential,” Physics Letters A, Vol. 372, No. 27-28, 2008, pp. 4779-4782. doi:10.1016/j.physleta.2008.05.030
|
[60]
|
A. F. Nikiforov and V. B. Uvarov, “Special Functions of Mathematical Physics,” Birkhauser, Bassel, 1988.
|
[61]
|
S. M. Ikhdair and R. Sever, “Exact Quantization Rule to the Kratzer-Type Potentials: An Application to the Diatomic Molecules,” Journal of Mathe-matical Chemistry, Vol. 45, No. 4, 2009, pp. 1137-1152.
doi:10.1007/s10910-008-9438-8
|
[62]
|
S. M. Ikhdair and R. Sever, “Solutions of the Spatially- Dependent Mass Dirac Equation with the Spin and Pseudospin Symmetry for the Cou-lomb-Like Potential,” Applied Mathematics and Computation, Vol. 216, No. 2, 2010, pp. 545-555. doi:10.1016/j.amc.2010.01.072
|
[63]
|
S. M. Ikhdair, C. Berk-demir and R. Sever, “Spin and Pseudospin Symmetry Along With Orbital Dependency of the Dirac- Hulthén Problem,” Applied Mathematics and Computation, Vol. 217, No. 22, 2011, pp. 9019-9032.
doi:10.1016/j.amc.2011.03.109
|
[64]
|
S. M. Ikhdair and R. Sever, “Bound-States of a Semi- Relativistic Equation for the PT-Symmetric Generalized Potential by the Nikiforov-Uvarov Method,” International Journal of Modern Physics E, Vol. 17, No. 6, 2008, pp. 1107-1123.
doi:10.1142/S0218301308010337
|
[65]
|
A. de Souza Dutra and G. Chen, “On Some Classes of Exactly-Solvable Klein-Gordon Equations,” Physics Letters A, Vol. 349, 2006, pp. 297-301.
doi:10.1016/j.physleta.2005.09.056
|
[66]
|
G. Chen, “Solutions of the Klein-Gordon for Exponential Scalar and Vector Poten-tials,” Physics Letters A, Vol. 339, 2005, pp. 300-303. doi:10.1016/j.physleta.2005.03.040
|
[67]
|
S. M. Ikhdair, “Rota-tion and Vibration of Diatomic Molecule in the Spa-tially-Dependent Mass Schrodinger Equation with Generalized q-Deformed Morse Potential,” Chemical Physics, Vol. 361, No. 1-2, 2009, pp. 9-17.
doi:10.1016/j.chemphys.2009.04.023
|
[68]
|
N. Saad, “The Klein-Gordon Equation with a Generalized Hulthén Potential in D-Dimensions,” Physica Scripta, Vol. 76, 2007, pp. 623-627.
doi:10.1088/0031-8949/76/6/005
|
[69]
|
W. C. Qiang, R. S. Zhou and Y. Gao, “Any -State Solutions of the Klein-Gordon Equation with the Generalized Hulthén Poten-tial,” Physics Letters A, Vol. 371, No. 3, 2007, pp. 201-204.
doi:10.1016/j.physleta.2007.04.109
|
[70]
|
S. M. Ikhdair and R. Sever, “Any -State Improved Quasi-Exact Analytical Solu-tions of the Spatially Dependent Mass Klein-Gordon Equation for the Scalar and Vector Hulthén Potentials,” Physica Scripta, Vol. 79, No. 3, 2009, pp. 035002-12.
doi:10.1088/0031-8949/79/03/035002
|
[71]
|
N. Rosen and P. M. Morse, “On the Vibrations of Polyatomic Molecules,” Physics Review, Vol. 42, No. 2, 1932, pp. 210-217. doi:10.1103/PhysRev.42.210
|
[72]
|
A. S. de Castro, “Klein-Gordon Particles in Mixed Vector-Scalar Inversely Linear Potentials,” Physics Letters A, Vol. 338, 2005, p. 81. doi:10.1016/j.physleta.2005.02.027
|
[73]
|
F. Cooper, A. Khare and U. P. Sukhatme, “Supersymmetry in Quantum Mechanics,” World Scientific, Singapore, 2001.
|
[74]
|
C. M. Bender and S. Boettcher, “Real Spectra in Non- Hermitian Hamiltonians Having PT Symmetry,” Physical Review Letters, Vol. 80, No. 24, 1998, pp. 5243-5246.
doi:10.1103/PhysRevLett.80.5243
|
[75]
|
C. B. C. Jasso, “Baryon Spectra in a Quark-Diquark Model with the Trigono-metric Rosen- Morse Potential,” MS Thesis (in Spanish), Insti-tute of Physics, Autonomous University of San Luis Potosi, México, 2005.
|
[76]
|
M. R. Spiegel, “Mathematical Handbook of Formulas and Tables,” McGraw-Hill Publishing Company, New York, 1968.
|
[77]
|
E. Eichten, K. Gottfried, T. Kinoshita, K.D. Lane and T.M. Yan, “Charmonium: Comparison with Experiment,” Physical Review D, Vol. 21, No. 1, 1980, pp. 203-233.
doi:10.1103/PhysRevD.21.203
|