Orateur
Dr
Pavel Kurasov
(Lund University)
Description
It is well-known that the celebrated Fermi delta potential model
[1,2] leads to
non-trivial scattering in the s-channel only. We propose
a new family of point interaction models which may be
used to describe particles with non-trivial interaction also
in the $p$-channel while preserving exact
solvability and point character of the interaction [3]. These
models are given by self-adjoint operators
and their spectral and scattering
properies are studied in detail.
The developed method is applied to the system of three
quantum particles and we discuss the possibillity that this
operator is semibounded (in contrast to the Landau Hamiltonian
studied by Minlos-Faddeev in the sixties[4]).
[1] F.A.Berezin, L.D.Faddeev,
Remark on the Schrödinger equation with singular potential.
(Russian) Dokl. Akad. Nauk SSSR, 137 (1961), 1011-1014.
[2] E. Fermi, Sul moto dei neutroni nelle sostanze idrogenate,
Ricerca Scientifica, 7 (1936), 13--52 (In Italian.), English translation in E.Fermi, Collected papers, vol. I, Italy 1921-1938, Univ. of Chicago Press, Chicago, 1962, pp. 980-1016.
[3] P. Kurasov, Triplet extensions I: semibounded operators in the scale of Hilbert spaces,
accepted for publication in J. d'Analyse Mathématique.
[4] R.A. Minlos and L.D. Faddeev, Comment on the problem of three particles with point interactions, Soviet Physics JETP, 14 (1962), 1315-1316.
Auteur principal
Dr
Pavel Kurasov
(Lund University)
