Perturbation theory of odd anharmonic oscillators. (English) Zbl 0446.47044


47F05 General theory of partial differential operators
47A55 Perturbation theory of linear operators
47B25 Linear symmetric and selfadjoint operators (unbounded)
Full Text: DOI


[1] Akhiezer, N.I.: The classical moment problem. Edinburgh: Oliver and Boyd 1965 · Zbl 0135.33803
[2] Akhiezer, N.I., Glazman, I.M.: Theory of linear operators in Hilbert space, Vol. II. New York: Ungar 1963 · Zbl 0098.30702
[3] Baslev, E., Combes, J.M.: Commun. Math. Phys.22, 280 (1971) · Zbl 0219.47005
[4] Bender, C.M., Wu, T.T.: Phys. Rev.184, 1231 (1969)
[5] Davydov, A.: Quantum mechanics. Oxford, New York: Pergamon Press 1965
[6] Gradshtein, I.S., Ryzhik, I.M.: Tables of series, integral, and products. New York: Academic Press 1964
[7] Graffi, S., Grecchi, V.: Commun. Math. Phys.62, 83 (1978)
[8] Hardy, G.H.: Divergent series. Oxford, UK: Oxford University Press 1947 · Zbl 0029.02505
[9] Herbst, I.W.: Commun. Math. Phys.64, 179 (1979) · Zbl 0447.47028
[10] Howland, J.S.: Pac. J. Math.55, 157 (1974)
[11] Kato, T.: Perturbation theory for linear operators. Berlin, Heidelberg, New York: Springer 1966 · Zbl 0148.12601
[12] Loeffel, J.J., Martin, A., Simon, B., Wightman, A.S.: Phys. Lett.30B, 656 (1969)
[13] Loeffel, J.J., Martin, A.: Proc. Programme 25th Conference, Strasbourg 1970
[14] Naimark, M.A.: Linear differential operators, Part II. London: Harrap 1964
[15] Reed, M., Simon, B.: Methods of modern mathematical physics, Vol. II. New York: Academic Press 1975 · Zbl 0308.47002
[16] Reed, M., Simon, B.: Methods of modern mathematical physics, Vol. IV. New York: Academic Press 1978 · Zbl 0401.47001
[17] Simon, B.: Ann. Phys.58, 76 (1970)
[18] Simon, B.: The definition of molecular resonance curves by the method of exterior complex scaling. Phys. Rev. Lett. (to appear)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.