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Analytical Solutions of the Kratzer-Fues Potential in an Arbitrary Number of Dimensions

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Foundations of Physics Letters

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Some aspects of the N dimensional Kratzer-Fues potential are discussed, which is an extension of the combined Coulomb-like potential with inverse quadratic potential in N dimensions. The analytical solutions obtained (eigenfunctions and eigenvalues) are dimensionally dependent, so also, the solutions depend on the value of the coefficient of the inverse quadratic term. The expectation values for < r−2 >, < r−1 > and the virial theorem for this potential are obtained and the values are also dimensions and parameter dependent.

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References

  1. 1. A. Erdelyi, Higher Transcendental Functions, Vol. 2 (McGraw-Hill, New York, 1953), p. 232.

    Google Scholar 

  2. 2. J. D. Louck, J. Mol. Spectroscopy 4, 298 (1960).

    Article  ADS  Google Scholar 

  3. 3. L. S. Davtyan, L. G. Mardoyan, G. S. Pogosyan, A. N. Sissakian, and V. M. Ter-Antonyan, J. Phys. A: Math. Gen. 20, 6121 (1987).

    Article  ADS  MathSciNet  Google Scholar 

  4. 4. B. Cordani, J. Phys. A: Math. Gen. 22, 2441 (1989).

    Article  ADS  MathSciNet  Google Scholar 

  5. 5. D. S. Bateman, C. Boyd, and B. Dutta-Roy, Am. J. Phys. 60(9), 833 (1992).

    Article  ADS  Google Scholar 

  6. 6. R. J. Yáñez, W. Assche, and J. Dehesa, Phys. Rev. A 50, 3065 (1994).

    Article  ADS  Google Scholar 

  7. 7. H. A. Mavromatis, Rep. on Math. Phys. 40(1), 17 (1997).

    Article  ADS  MathSciNet  Google Scholar 

  8. 8. Zeng Gao-Jian, Zhou Shi-Lun, Ao Sheng-Mei, and Jiang Fa-Sheng, J. Phys. A: Math. Gen. 30, 1775 (1997).

    Article  ADS  Google Scholar 

  9. 9. J. L. A. Coelho and R. L. P. G. Amaral, J. Phys. A: Math. Gen. 35, 5255 (2002).

    Article  ADS  MathSciNet  Google Scholar 

  10. 10. J. L. Cardoso and R. Álvarez-Nodarse, J. Phys. A: Math. Gen. 36, 2055 (2003).

    Article  ADS  Google Scholar 

  11. 11. P. Pradhan, Am. J. Phys. 63, 664 (1995).

    Article  ADS  Google Scholar 

  12. 12. H. A. Mavromatis, Am. J. Phys. 64, 1074 (1996).

    Article  ADS  Google Scholar 

  13. 13. H. Fukutaka and T. Kashiwa, Ann. Phys. 176, 301 (1987).

    Article  ADS  MathSciNet  Google Scholar 

  14. 14. C. Grosche and F. Steiner, Z. Phys. C 36, 699 (1987).

    Article  ADS  MathSciNet  Google Scholar 

  15. 15. C. Grosche and F. Steiner, J. Math. Phys. 36(5), 2354 (1998); Handbook of Feynman Path Integrals (Springer, Berlin, 1998), p. 99.

    Article  ADS  MathSciNet  Google Scholar 

  16. 16. S. Al-Jaber, Nuovo Cimento B 112, 761 (1997).

    Google Scholar 

  17. 17. S. Al-Jaber, Intern. J. Theor. Phys. 37(4), 1289 (1998).

    Article  Google Scholar 

  18. 18. G. Esposito, Found. Phys. Lett. 11(6), 535 (1998).

    Article  MathSciNet  Google Scholar 

  19. 19. Shi-Hai Dong, Found. Phys. Lett. 15(4), 385 (2002).

    Article  MathSciNet  Google Scholar 

  20. 20. Lu-Ya Wang, Xiao-Yan Gu, Zhong-Qi Ma, and Shi-Hai Dong, Found. Phys. Lett. 15(6), 569 (2002).

    Article  MathSciNet  Google Scholar 

  21. 21. Xiao-Yan Gu, Bin Duan, and Zhong-Qi Ma, J. Math. Phys. 43(6), 2895 (2002).

    Article  ADS  MathSciNet  Google Scholar 

  22. 22. Shi-Hai Dong and Zhong-Qi Ma, Phys. Rev. A 65, 042717 (2002).

    Article  ADS  Google Scholar 

  23. 23. Shi-Hai Dong, Xiao-Yan Gu, Zhong-Qi Ma, and Jiang Yu, Int. J. Mod. Phys. E 12(4), 555 (2003).

    Article  ADS  Google Scholar 

  24. 24. Shi-Hai Dong, Guo-Hua Sun, and D. Popov, J. Math. Phys. 44(10), 4467 (2003).

    Article  ADS  MathSciNet  Google Scholar 

  25. 25. Shi-Hai Dong, J. Phys. A: Math. Gen. 36, 4977 (2003).

    Article  ADS  Google Scholar 

  26. 26. K. J. Oyewumi and E. A. Bangudu, Arabian J. Sci. Eng. 28(2A), 173 (2003).

    MathSciNet  Google Scholar 

  27. 27. A. Kratzer, Z. Phys. 3, 289 (1920).

    Article  ADS  Google Scholar 

  28. 28. E. Fues, Ann. Physik 80, 367 (1926).

    Article  ADS  Google Scholar 

  29. 29. I. I. Gol’dman, V. D. Krivchenkov, V. I. Kogan, and V. M. Galitskii, Problems in Quantum Mechanics (Academic, New York, 1960), p. 308.

    Google Scholar 

  30. 30. S. Flügge, Practical Quantum Mechanics (Springer, Berlin, 1994), p. 178.

    Google Scholar 

  31. 31. L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Non-Relativistic Theory): Course of Theoretical Physics 3, 3rd edn. (Butterworth-Heinemann, Oxford, 1999), p. 127.

    Google Scholar 

  32. 32. R. N. Kesarwani and Y. P. Varshin, Chem. Phys. Lett. 93, 545 (1982).

    Article  ADS  Google Scholar 

  33. 33. F. M. Fernández, A. López Piñeiro and B. Moreno, J. Phys. A: Math. Gen. 27, 5013 (1994).

    Article  ADS  Google Scholar 

  34. 34. M. Robnik and L. Salansnich, J. Phys. A: Math. Gen. 30, 1719 (1997).

    Article  ADS  Google Scholar 

  35. 35. R. L. Hall and N. Saad, J. Chem. Phys. 109(8), 2983 (1998).

    Article  ADS  Google Scholar 

  36. 36. M. Znojil, J. Math. Chem. 26, 157 (1999).

    Article  MathSciNet  Google Scholar 

  37. 37. H. A. Mavromatis, Am. J. Phys. 66(4), 335 (1998).

    Article  ADS  MathSciNet  Google Scholar 

  38. 38. A. Chatterjee, Phys. Rep. 186, 249 (1990).

    Article  ADS  Google Scholar 

  39. 39. J. Avery, Hyperspherical Harmonics: Applications in Quantum Theory (Kluwer Academic, Dordrecht, 1989).

    Book  MATH  Google Scholar 

  40. 40. N. Shimakura, Partial Differential Operators of Elliptic Type (American Mathematical Society, Providence, Rhode Island, 1992).

    MATH  Google Scholar 

  41. 41. S. Rosati, Hyperspherical Harmonics Methods for Strongly Interacting Systems: A Summary and New Developments I and II (SMR1348, The Second European Summer School on Microscopic Quantum Many-Body Theories and Their Applications, ICTP Lecture Notes, 2002).

  42. 42. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formula, Graphs and Mathematical Tables (Dover, New York, 1970).

    MATH  Google Scholar 

  43. 43. E. Merzbacher, Quantum Mechanics, 3rd edn. (Wiley, New York, 1998).

    MATH  Google Scholar 

  44. 44. G. Marc and W. G. McMillan, Adv. Chem. Phys. 58, 205 (1985).

    Google Scholar 

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  1. Department of Physics, University of Ilorin, P. M. B. 1515, Ilorin, Nigeria

    K. J. Oyewumi

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  1. K. J. Oyewumi
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Oyewumi, K. Analytical Solutions of the Kratzer-Fues Potential in an Arbitrary Number of Dimensions. Found Phys Lett 18, 75–84 (2005). https://doi.org/10.1007/s10702-005-2481-9

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  • DOI: https://doi.org/10.1007/s10702-005-2481-9

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