Abstract
Let H 0 be the Hamiltonian of an unperturbed oscillating system and let V be a small perturbation which we take to be analytic in a neighbourhood of the surface H 0 = E > 0. If H = H 0 + λV is the total Hamiltonian than there is a convergent perturbation expansion near λ = 0 of the form
when applied to test function which are analytic near H 0 = E. In (1) δ (H - E) is the Dirac1 distribution concentrated on the surface H = E and δ (n) H 0 - E) are the derivatives of the Dirac distribution on the unperturbed surface H 0 = E.
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References
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© 1993 Springer Science+Business Media New York
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Constantinescu, F. (1993). Perturbation Expansion for Distributions on Surfaces, Lagrange-Bürmann Theorem and Applications to Mechanics. In: Pathak, R.S. (eds) Generalized Functions and Their Applications. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-1591-7_5
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DOI: https://doi.org/10.1007/978-1-4899-1591-7_5
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