Abstract
We study a general class of confinement potentials in Schrödinger theory using the analytic theory of continued fractions. We construct an infinite continued fraction representation for the Green's function and study its convergence, its analytic properties in the major coupling constant and its relation to the perturbation series. We prove the existence of normalizable confined state eigensolutions with equally spaced energy levels if certain constraints on the coupling constants of the theory are satisfied: we also show that under a separate set of constraints neither bound nor confined states exist.
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
References
EichtenE., GottfriedK., KinoshitaT. LaneK., and YanT-M.,Phys. Rev. Lett. 36, 500 (1976).
CasherA., KogutJ., and SuskindL.,Phys. Rev. D10, 732 (1974). See also R.F. Dashen in ‘Proceedings of the 1975 International Symposium on Lepton and Photon Interactions at High Energy’ Stanford, August 21–27, 1975.
Singh, V., Biswas, S.N., and Datta, K.,Phys. Rev. D (1978) (To be published).
WallH.S.,Analytic Theory of Continued Fractions, D. Van Nostrand Co., New York, 1948, Theorem 28.1, p. 120.
Stielties, T.J., ‘Recherches sur les fractions continues’,Oeuvres Vol. 2, p. 402;Comptes Rendus CXVIII (1401) 1894.
Wall, H.S.,Ibid, Equation 92.15, p. 358.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Singh, V., Biswas, S.N. & Datta, K. Analytic continued fraction theory for a class of confinement potentials. Lett Math Phys 3, 73–81 (1979). https://doi.org/10.1007/BF00959542
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00959542