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Solution of the wave equation for the logarithmic potential with application to particle spectroscopy
1.L. M. Lederman, Proceedings of the 1977 International Symposium on Lepton and Photon Interactions at High Energies, edited by F. Gutbrod, DESY, Hamburg, 1977, p. 567.
2.C. Quigg and J. L. Rosner, Phys. Lett. B 71, 153 (1977).
3.C. Quigg and J. L. Rosner, Phys. Lett. B 72, 462 (1978).
4.H. B. Thacker, C. Quigg, and J. L. Rosner, Phys. Lett. B 74, 350 (1978).
5.For the generalized power potential the eigenenergies and Regge trajectories have been calculated by S. K. Bose, A. Jabs, and H. J. W. Müller‐Kirsten, Phys. Rev. D 13, 1489 (1976).
6.C. Quigg and J. L. Rosner, Fermilab‐Pub‐77/106‐THY, 1977, and Fermilab‐Pub‐78/19‐THY, 1978 (unpublished).
7.For the Mathieu equation see, for instance, R. B. Dingle and H. J. W. Müller, J. F. Reine U. Angew. Math. 221, 11 (1962)
7.and H. A. Aly, H. J. W. Müller‐Kirsten, and N. Vahedi‐Fardi, J. Math. Phys. 16, 961 (1975).
7.However, the Mathieu equation is exceptionally simple. Our procedure here therefore parallels that developed for the more complicated case of the Gauss potential, H. J. W. Müller, J. Math. Phys. 11, 355 (1970).
8.F. Gesztesy and L. Pittner, University of Graz preprint UTP‐04/77, 1977, to appear in J. Phys. A. These authors investigate the logarithmic potential with a view for application to the calculation of electron interferences observed in “Fresnel biprisma experiments” in which electrons are used instead of light and suitable electric fields instead of the optical lens.
9.The same procedure has been applied previously to several other cases, such as the Schrödinger equation for a Gauss potential [H. J. W. Müller, J. Math. Phys. 11, 355 (1970)]
9.and the ellipsoidal wave equation [H. J. W. Müller, Math. Nachr. 31, 89 (1966)].
10.H. J. W. Müller‐Kirsten and N. Vahedi, Phys. Rev. D 14, 3079 (1976).
11.L. D. Landau and E. M. Lifshitz, Relativistic Quantum Theory (Pergamon, New York, 1971), p. 288.
12.H. J. W. Müller‐Kirsten, G. E. Hite, and S. K. Bose, “Explicit solution of the wave equation for arbitrary power potentials with application to charmonium spectroscopy,” University of Kaiserslautern preprint, 1978, unpublished.
13.For the explicit normalization of these wavefunctions see R. S. Kaushal and H. J. W. Müller‐Kirsten, “Explicit normalization of boundstate wavefunctions and the calculation of decay widths,” University of Kaiserslautern preprint, 1979, unpublished.
14.H. J. W. Müller, Ann. Phys. (Leipz.) 15, 395 (1965);
14.H. J. W. Müller, Physica 31, 688 (1965);
14.H. J. W. Müller and K. Schilcher, J. Math. Phys. 9, 255 (1968);
14.H. J. W. Müller‐Kirsten and N. Vahedi‐Faridi, J. Math. Phys. 14, 1291 (1973).
15.J. Boukema, Physica 30, 1320, 1909 (1964).
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