Abstract
A modified Rayleigh-Schrödinger perturbation method is used to derive explicit expansions for the eigenvalues and eigensolutions of the anharmonic oscillator. We then point out the dual relationship between the anharmonic oscillator and the Schrödinger equation for a Yukawa potential. Finally we consider an application of the method to a field-theoretic Hamiltonian, since the anharmonic oscillator plays a dominant role in many field-theoretic models.
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The author is indebted to Professors A. B.Zahlan and H. H.Aly for offering him a visiting professorship in their department at the American University of Beirut where this work was done.
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Müller, H.J.W. On the anharmonic oscillator in quantum mechanics and in field theory. Z. Physik 205, 149–158 (1967). https://doi.org/10.1007/BF01333367
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DOI: https://doi.org/10.1007/BF01333367