Abstract
By applying Extended Transformation method we have generated exact solution of D-dimensional radial Schrödinger equation for a set of power-law multi-term potentials taking singular potentials $$V(r) = ar^{ - \tfrac{1} {2}} + br^{ - \tfrac{3} {2}}$$, $$V(r) = ar^{\tfrac{2} {3}} + br^{ - \tfrac{2} {3}} + cr^{ - \tfrac{4} {3}}$$, V(r) = ar + br −1 + cr 2 and V(r) = ar 2+br −2+cr −4+dr −6 as input reference. The restriction on the parameters of the given potentials and angular momentum quantum number ℓ are obtained. The multiplet structure of the generated exactly solvable potentials are also shown.
[1] A. Bhattacharjie, E. C. G. Sudarshan, Nuovo Cimento 25, 864 (1962) http://dx.doi.org/10.1007/BF0273315310.1007/BF02733153Search in Google Scholar
[2] L. D. Landau, E. M. Lifshitz, Quantum Mechanics: Non-Relativistic Theory, 3rd ed., (Pergamon, New York, 1977) Search in Google Scholar
[3] A. F. Nikiforov, V. B. Uvarov, Special Functions of Mathematical Physics, (Birkhauser, Basel, 1988) http://dx.doi.org/10.1007/978-1-4757-1595-810.1007/978-1-4757-1595-8Search in Google Scholar
[4] R. S. Kaushal Phys. Lett. A 142, 57 (1989) http://dx.doi.org/10.1016/0375-9601(89)90158-810.1016/0375-9601(89)90158-8Search in Google Scholar
[5] R. S. Kaushal, Ann. Phys. (N.Y.) 206, 90 (1991) http://dx.doi.org/10.1016/0003-4916(91)90222-T10.1016/0003-4916(91)90222-TSearch in Google Scholar
[6] M. Znojil, J. Math. Phys. 30, 23 (1989) http://dx.doi.org/10.1063/1.52861410.1063/1.528614Search in Google Scholar
[7] S. A. S. Ahmed, Int. J. Theor. Phys. 36, 1893 (1997) http://dx.doi.org/10.1007/BF0243585110.1007/BF02435851Search in Google Scholar
[8] F. Cooper, J. N. Ginocchio, A. Khare, Phys. Rev. D 36, 2458 (1987) http://dx.doi.org/10.1103/PhysRevD.36.245810.1103/PhysRevD.36.2458Search in Google Scholar
[9] O. Bayrak, I. Boztosun, H. Ciftci, Int. J. Quantum Chem. 107, 540 (2007) http://dx.doi.org/10.1002/qua.2114110.1002/qua.21141Search in Google Scholar
[10] M. Znojil, J. Math. Phys. 31, 108 (1990) http://dx.doi.org/10.1063/1.52886710.1063/1.528867Search in Google Scholar
[11] S. Ozcelik, M. Simsek, Phys. Lett. A 152, 145 (1991) http://dx.doi.org/10.1016/0375-9601(91)91081-N10.1016/0375-9601(91)91081-NSearch in Google Scholar
[12] S. K. Bose, Nuovo Cimento B 109, 1217 (1994) http://dx.doi.org/10.1007/BF0272668510.1007/BF02726685Search in Google Scholar
[13] Y. P. Varshni, Phys. Lett. A 183, 9 (1993) http://dx.doi.org/10.1016/0375-9601(93)90879-510.1016/0375-9601(93)90879-5Search in Google Scholar
[14] S. Fubini, R. Stroffolini, Nuovo Cimento 37, 1812 (1965) http://dx.doi.org/10.1007/BF0278339210.1007/BF02783392Search in Google Scholar
[15] G. Esposito, J. Phys. A 31, 9493 (1998) http://dx.doi.org/10.1088/0305-4470/31/47/01010.1088/0305-4470/31/47/010Search in Google Scholar
[16] S. H. Dong, Z. Q. Ma, J. Phys. A 31, 9855 (1998) http://dx.doi.org/10.1088/0305-4470/31/49/00910.1088/0305-4470/31/49/009Search in Google Scholar
[17] S. H. Dong, Z. Q. Ma and G. Esposito, Found. Phys. Lett. 12, 465 (1999) http://dx.doi.org/10.1023/A:102163341161610.1023/A:1021633411616Search in Google Scholar
[18] A. O. Barut, M. Berrondo, G. Garcia-Calderon, J. Math. Phys. 21, 1851 (1980) http://dx.doi.org/10.1063/1.52460110.1063/1.524601Search in Google Scholar
[19] S. H. Dong, G. H. San, Found. Phys. Lett. 16, 357 (2003) http://dx.doi.org/10.1023/A:102531380947810.1023/A:1025313809478Search in Google Scholar
[20] S. H. Dong, Int. J. Theor. Phys. 39, 1119 (2000) http://dx.doi.org/10.1023/A:100361481093410.1023/A:1003614810934Search in Google Scholar
[21] S. H. Dong, Phys. Scr. 64, 273 (2001) http://dx.doi.org/10.1238/Physica.Regular.064a0027310.1238/Physica.Regular.064a00273Search in Google Scholar
[22] S. H. Dong, Phys. Scr. 65, 289 (2002) http://dx.doi.org/10.1238/Physica.Regular.065a0028910.1238/Physica.Regular.065a00289Search in Google Scholar
[23] S. H. Dong, G. H. San, Phys. Scr. 70, 94 (2004) http://dx.doi.org/10.1088/0031-8949/70/2-3/00410.1088/0031-8949/70/2-3/004Search in Google Scholar
[24] H. Hassanabadi, A. A. Rajabi, Phys. Lett. A 373, 679 (2009) http://dx.doi.org/10.1016/j.physleta.2008.12.03810.1016/j.physleta.2008.12.038Search in Google Scholar
[25] S. M. Ikhdair, R. Sever, Cent. Eur. J. Phys. 5, 516 (2007) http://dx.doi.org/10.2478/s11534-007-0022-910.2478/s11534-007-0022-9Search in Google Scholar
[26] R. Kumar, F. Chand, Phys. Scr. 85, 055008 (2012) http://dx.doi.org/10.1088/0031-8949/85/05/05500810.1088/0031-8949/85/05/055008Search in Google Scholar
[27] G. R. Khan, Eur. Phys. J. D 53, 123 (2009) http://dx.doi.org/10.1140/epjd/e2009-00096-610.1140/epjd/e2009-00096-6Search in Google Scholar
[28] S. A. S. Ahmed, B. C. Borah, D. Sharma, Eur. Phys. J. D 17, 5 (2001) http://dx.doi.org/10.1007/s10053017003210.1007/s100530170032Search in Google Scholar
[29] N. Saikia, S. A. S. Ahmed, Phys. Scr. 81, 035006 (2010) http://dx.doi.org/10.1088/0031-8949/81/03/03500610.1088/0031-8949/81/03/035006Search in Google Scholar
[30] N. Saikia, S. A. S. Ahmed, Lat. Am. J. Phys. Educ. 4, 61 (2010) Search in Google Scholar
[31] N. Saikia, S. A. S. Ahmed, Theor. Math. Phys. 171, 490 (2012) http://dx.doi.org/10.1007/s11232-012-0047-010.1007/s11232-012-0047-0Search in Google Scholar
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