Abstract
By carrying out a general analysis of properties of the wave operators for the non-unitary scattering theory which arises in connection with the use of complex ”optical“ potentials in nuclear scattering and elsewhere, we clarify some puzzling differences between two recent approaches to this subject.
Similar content being viewed by others
References
Davis, E.B.: Two-channel Hamiltonians and the optical model of nuclear scattering. Ann. Inst. H. Poincaré 29A, 395–413 (1978)
Davies, E.B.: Non-unitary scattering and capture. II. Dynamical semigroup theory. To appear
Davies, E.B.: One-parameter semigroups. London, New York: Academic Press 1980
Dowson, H.R.: Spectral theory of linear operators. London Math. Soc. Monographs. London, New York: Academic Press 1978
Dunford, N., Schwartz, J.T.: Linear operators Part 3. Spectral operators. Wiley-Interscience, 1971
Goldstein, C.: Perturbation of non-self-adjoint operators. I. Arch. Rat. Mech. Anal.37, 268–296 (1970); II. Arch. Rat. Mech. Anal.42, 380–402 (1971)
Kato, T.: Perturbation theory for linear operators. 1st Edition. Berlin, Heidelberg, New York: Springer 1966
Martin, Ph.A.: Scattering theory with dissipative interactions and time decay. Nuovo Cimento30B, 217–238 (1975)
Reed, M., Simon, B.: Methods of modern mathematical physics Vol. 3. London, New York: Academic Press 1978
Reed, M., Simon, B.: Methods of modern mathematical physics Vol. 4. London, New York: Academic Press 1978
Sergent, P., Coudray, C.: The inverse problem at fixed energy for finite range complex potentials. Ann. Inst. H. Poincaré29A, 179–205 (1978)
Simon, B.: Phase space analysis of simple scattering systems: extensions of some work of Enss. Duke Math. J.46, 119–168 (1979)
Sz.-Nagy, B., Foias, C.: Harmonic analysis of operators on Hilbert space. Amsterdam: North-Holland 1970
Author information
Authors and Affiliations
Additional information
Communicated by B. Simon
Rights and permissions
About this article
Cite this article
Davies, E.B. Non-unitary scattering and capture. I. Hilbert space theory. Commun.Math. Phys. 71, 277–288 (1980). https://doi.org/10.1007/BF01197295
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01197295