Abstract
The perturbation method for bound states within the framework of the Shifman-Vainshtein-Zakharov sum rule method is studied on simple systems (linear harmonic oscillator, hydrogen atom) in external electric fields. It is pointed out that for stronger fields reasonable results for the ground-state energy can only be achieved when sum rules are written for the correction to the Euclidean Green function caused by the external field. Moreover, if the system is bound by a singular (Coulomb) potential, one needs to sum higher perturbative corrections to the Green function and to find a realistic approximation of the continuum contribution to the sum rules. The results are of relevance e.g. for calculations of nucleon magnetic moments and toponium properties via SVZ sum rules in QCD.
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We are grateful to Prof. J. Pišút for constructive remarks, discussions, and for reading of and comments on the manuscript. We also acknowledge discussions with Prof. H. Leutwyler during the Hadron Structure '84 Conference at Smolenice, where preliminary results of this work had been reported.
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Novák, I., Olejník, Š. Bound-state perturbation method via SVZ sum rules in quantum mechanics. Czech J Phys 35, 1067–1083 (1985). https://doi.org/10.1007/BF01596425
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DOI: https://doi.org/10.1007/BF01596425