Scattering theory for finitely many sphere interactions supported by concentric spheres

Journal Article · Sun Jun 01 04:00:00 EDT 1997 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.532022· OSTI ID:503617

Hounkonnou, M N; Hounkpe, M ^[1]; Shabani, J ^[2]

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1. Institut de Mathematiques et de Sciences Physiques, Universite Nationale du Benin, BP 613 Porto-Novo (Benin)
2. UNESCO Nairobi Office, P. O. Box 30592 Nairobi (Kenya)

We study stationary scattering theory for finitely many sphere interactions formally given by the Hamiltonian H={minus}{Delta}+{summation}{sub j=1}{sup N}{alpha}{sub j}{delta}({vert_bar}x{vert_bar}{minus}R{sub j}) and its generalizations to the case of interactions of the second type and interactions with nonseparated boundary conditions. In a previous publication [J. Math. Phys. {bold 29}, 660{endash}664 (1988)], it was shown that the self-adjoint Hamiltonian H{sub {l_brace}{alpha}{sub l}{r_brace},{l_brace}R{r_brace}} corresponding to H may be defined as a limit in norm resolvent convergence of a family H{sub {var_epsilon}} of local scaled short-range Hamiltonians. In this paper we also study scattering theory corresponding to H{sub {var_epsilon}} and show that the scattering quantities associated with H{sub {var_epsilon}} converge to those of H{sub {l_brace}{alpha}{sub l}{r_brace},{l_brace}R{r_brace}} as {var_epsilon}{r_arrow}0. {copyright} {ital 1997 American Institute of Physics.}

• OSTI ID: 503617
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 6 Vol. 38; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
BOUNDARY CONDITIONS
CONVERGENCE
HAMILTONIANS
POTENTIAL SCATTERING
SCATTERING