Analytical Approximation to the ℓ-Wave Solutions of the Hulthén Potential in Tridiagonal Representation
ZHANG Min-Cang1**, HUANG-FU Guo-Qing 2
1College of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062 2Department of Physics and Electronic Engineering, Weinan Teachers University, Weinan 714000
Analytical Approximation to the ℓ-Wave Solutions of the Hulthén Potential in Tridiagonal Representation
ZHANG Min-Cang1**, HUANG-FU Guo-Qing 2
1College of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062 2Department of Physics and Electronic Engineering, Weinan Teachers University, Weinan 714000
摘要The Schrödinger equation with the Hulthén potential is studied by working in a complete square integrable basis that carries a tridiagonal matrix representation of the wave operator. The arbitrary ℓ-wave solutions are obtained by using an approximation of the centrifugal term. The resulting three-term recursion relation for the expansion coefficients of the wavefunction is presented and the wavefunctions are expressed in terms of the Jacobi polynomial. The discrete spectrum of the bound states is obtained by the diagonalization of the recursion relation.
Abstract：The Schrödinger equation with the Hulthén potential is studied by working in a complete square integrable basis that carries a tridiagonal matrix representation of the wave operator. The arbitrary ℓ-wave solutions are obtained by using an approximation of the centrifugal term. The resulting three-term recursion relation for the expansion coefficients of the wavefunction is presented and the wavefunctions are expressed in terms of the Jacobi polynomial. The discrete spectrum of the bound states is obtained by the diagonalization of the recursion relation.
ZHANG Min-Cang**;HUANG-FU Guo-Qing
. Analytical Approximation to the ℓ-Wave Solutions of the Hulthén Potential in Tridiagonal Representation[J]. 中国物理快报, 2011, 28(5): 50304-050304.
ZHANG Min-Cang**, HUANG-FU Guo-Qing
. Analytical Approximation to the ℓ-Wave Solutions of the Hulthén Potential in Tridiagonal Representation. Chin. Phys. Lett., 2011, 28(5): 50304-050304.
[1] Schiff L I 1955 Quantum Mechanics 3nd end (New York: McGraw-Hill)
[2] Flügge S 1974 Practical Quantum Mechanics (Berlin: Springer)
[3] Bahlouli H and Alhaidari A D 2010 Physica Scripta 81 025008
[4] Alhaidari A D 2007 J. Phys. A: Math. Theor. 40 6305
de Souza-Dutra A 1993 Phys. Rev. A 47 R2435
Nag N, Roychoudhury R and Varshni Y P1994 Phys. Rev. A 49 5098
Dutt R, Khare A and Varshni Y P1995 J. Phys. A: Math. Gen. 28 L107
[5] Infeld L and Hull T D 1951 Rev. Mod. Phys. 23 21
[6] Dong S H 2007 Factorization Method in Quantum Mechanics (Berlin: Springer)
[7] Bander M and Itzykson C 1968 Rev. Mod. Phys. 38 330
Alhassid Y, Gursey F and Iachello F 1983 Phys. Rev. Lett. 50 873
[8] Cooper F, Khare A and Sukhatme U 1995 Phys. Rep. 251 267
[9] Greene R L and Aldrich C 1976 Phys. Rev. A 14 2363
[10] Alhaidari A D 2005 J. Phys. A: Math. Gen. 38 3409
Alhaidari A D 2008 Ann. Phys. 323 1709
Alhaidari A D and Bahlouli H 2008 Phys. Rev. Lett. 100 110401
[11] Alhaidari A D 2007 J. Phys. A: Math. Theor. 40 14843
[12] Alhaidari A D 2010 Physica Scripta 81 025013
[13] Bahlouli H, Abdelmonem M S and Nasser I M 2010 Physica Scripta 82 065005
[14] Alhaidari A D 2005 Ann. Phys. 317 152
El Aaoud E, Bahlouli H and Alhaidari A D 2008 Int. Rev. Phys. 2 5
[15] Zhang M C and An B 2010 Chin. Phys. Lett. 27 110301
[16] Hulthén L 1942 Ark. Mat. Astron. Fys. A 28 5
[17] Lam C S and Varshni Y P 1971 Phys. Rev. A 4 1875
[18] Hall R L1985 Phys. Rev. A 32 14
[19] Tietz T1961 J. Chem. Phys. 35 1917
[20] Lindhard J and Hansen P G 1986 Phys. Rev. Lett. 57 965
[21] Gönül B, Özer O, Cançelik Y and Koçak M 2000 Phys. Lett. A 275 238
2011, Vol. 28 
