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On limits of separable potentials and operator extensions

Authors
  • Breitenecker, M.
  • Gruemm, H.R.
Publication Date
Jan 01, 1969
Identifiers
DOI: 10.1007/BF01645532
OAI: oai:inspirehep.net:58923
Source
INSPIRE-HEP
License
Unknown
External links

Abstract

A family of self-adjoint Hamiltonians with a separable potential leading towards a contact potential (zero range) is analyzed by tools of functional analysis. It is shown that the family of time evolution operatorse−iHt converges strongly (for allt) though the family of Hamiltonians does not converge even weakly. In the case of three dimensions a renormalization procedure is discussed and a correspondence between the renormalized coupling constant and the self-adjoint extensions of the free Hamiltonian is established.

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