Non-central potentials, exact solutions and Laplace transform approach
- 155 Downloads
Exact bound state solutions and the corresponding wave functions of the Schrödinger equation for some non-central potentials including Makarov potential, modified-Kratzer plus a ring-shaped potential, double ring-shaped Kratzer potential, modified non-central potential and ring-shaped non-spherical oscillator potential are obtained by using the Laplace transform approach. The energy spectrums of the Hartmann potential, modified-Kratzer potential and ring-shaped oscillator potential are also briefly studied as special cases. It is seen that our analytical results for all these potentials are consistent with those obtained by other works. We also give some numerical results obtained for the modified non-central potential for different values of the related quantum numbers.
KeywordsExact solution Laplace transform Non-central potential Schrödinger equation
Unable to display preview. Download preview PDF.
- 2.Cang Z.M., Bang W.Z.: Chem. Phys. 16, 1863 (2007)Google Scholar
- 6.R. Dutt, A. Gangopadhyaya, U.P. Sukhatme, Am. J. Phys. 65, 400 (1997), [arXiv: hep-th/9611087].Google Scholar
- 14.Dong C.Z.: J. Atom. Mol. Phys. 22, 483 (2005)Google Scholar
- 16.F. Yasuk, İ. Boztosun, A. Durmus, [arXiv: quant-ph/0605007]Google Scholar
- 17.Flü S.: Practical Quantum Mechanics I. Springer, Berlin, Heidelberg, New York, NY (1971)Google Scholar
- 20.A. Arda, R. Sever, J. Math. Chem. doi: 10.1007/s10910-011-9944-y (in press)
- 24.Spiegel M.R.: Schaum’s Outline of Theory and Problems of Laplace Transforms. Schaum, New York, NY (1965)Google Scholar
- 25.Abramowitz M., Stegun I.A.: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover, New York, NY (1965)Google Scholar