Abstract
We prove that the spectrum for a large class ofN-body Stark Hamiltonians is purely absolutely continuous. We need slow decay at infinity and local singularities of at most Coulomb type. In particular our results include the usual models for atoms and molecules.
Similar content being viewed by others
References
[A] Agmon, S.: Private communication
[ABG] Amrein, W.O., Boutet de Monvel, A.M., Georgescu, V.: Notes on the N-body problem; Part I. Preprint Univ. de Geneve UGVA DPT 1988/11-598a
[AHS] Agmon, S., Herbst, I., Skibsted, E.: Perturbation of embedded eigenvalues in the generalized N-body problem. Commun. Math. Phys.122, 411–438 (1989)
[AS] Abramowitz, M., Stegun, I.A. (eds.): Handbook of mathematical functions. AMS55, Department of Commerce, National Bureau of Standards, 1964
[D] Derezinski, J.: Asymptotic completeness of long range N-body quantum systems. Ann. Math.138, 427–476 (1993)
[FH] Froese, R., Herbst I.: Exponential bounds and absence of positive eigenvalues for N-body Schrödinger operators. Commun. Math. Phys.87, 429–447 (1982)
[H1] Herbst, I.: Temporal exponential decay for the Stark effect in atoms. J. Funct. Anal.48, 224–251 (1982)
[H2] Herbst, I.: Perturbation theory for the decay rate of eigenfunctions in the generalized N-body problem. Commun. Math. Phys.158, 517–536 (1993)
[HMS2] Herbst, I., Møller, J.S., Skibsted, E.: Asymptotic completeness of N-body Stark Hamiltonians. To appear in Commun. Math. Phys.
[HS] Halmos, P.R., Sunder, V.S.: Bounded Integral Operators onL 2 spaces. Berlin Heidelberg New York: Springer, 1978
[IO] Iorio, R.J. Jr., O'Carroll, M.: Asymptotic completeness for multi-particle Schroedinger Hamiltonians with weak potentials. Commun. Math. Phys.27, 137–145 (1972)
[K] Korotyaev, E.L.: On the scattering theory of several particles in an external electric field. Math. USSR Sb.60, 177–196 (1988)
[M] Mourre, E.: Absence of singular continuous spectrum for certain selfadjoint operators. Commun. Math. Phys.91, 391–408 (1981)
[PSS] Perry, P., Sigal, I.M., Simon, B.: Spectral analysis of N-body Schrödinger operators. Ann. Math.114, 519–567 (1981)
[RS] Reed, M., Simon, B.: Analysis of operators. Methods of modern mathematical physics IV, New York: Academic Press, 1978
[Si] Sigal, I.M.: Stark effect in multielectron systems: Non-existence of bound states. Commun. Math. Phys.122, 1–22 (1989)
[Sk] Skibsted, E.: Absolute spectral continuity for N-body Stark Hamiltonians. Ann. Inst. Henri Poincaré61, 2, 223–243 (1994)
[T1] Tamura, H.: Spectral and scattering theory for 3-particle Hamiltonian with Stark effect: Asymptotic completeness. Osaka J. Math.29, 135–159 (1992)
[T2] Tamura, H.: Spectral and Scattering Theory for 3-Particle Hamiltonian with Stark effect: Non-existence of Bound States and Resolvent Estimate. Preprint 1993
[T3] Tamura, H.: Spectral analysis for N-particle systems with Stark effect: Non-existence of bound states and principle of limiting absorption. Preprint 1993
[T4] Tamura, H.: Principle of Limiting Absorption for N-body Schrödinger Operators. Lett. Math. Phys.17, 31–36 (1989)
Author information
Authors and Affiliations
Additional information
Communicated by B. Simon
Research partially supported by NSF grant DMS 9307147.
Rights and permissions
About this article
Cite this article
Herbst, I., Møller, J.S. & Skibsted, E. Spectral analysis ofN-body Stark Hamiltonians. Commun.Math. Phys. 174, 261–294 (1995). https://doi.org/10.1007/BF02099603
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02099603