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Author Zorbas, J.
Source United States Department of Energy Office of Scientific and Technical Information
Content type Text
Language English
Subject Keyword CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS ♦ QUANTUM MECHANICS ♦ SCATTERING ♦ GREEN FUNCTION ♦ HAMILTONIANS ♦ HILBERT SPACE ♦ MATHEMATICAL OPERATORS ♦ WAVE FUNCTIONS ♦ BANACH SPACE ♦ FUNCTIONS ♦ MATHEMATICAL SPACE ♦ MECHANICS ♦ QUANTUM OPERATORS ♦ SPACE ♦ Theoretical & Mathematical Physics- Classical & Quantum Mechanics
Abstract The existence of a family of self-adjoint Hamiltonians H/sub theta/, theta element of (0, 2..pi..), corresponding to the formal expression H/sub 0/+..nu..delta (x) is shown for a general class of self-adjoint operators H/sub 0/. Expressions for the Green's function and wavefunction corresponding to H/sub theta/ are obtained in terms of the Green's function and wavefunction corresponding to H/sub 0/. Similar results are shown for the perturbation of H/sub 0/ by a finite sum of Dirac distributions. A prescription is given for obtaining H/sub theta/ as the strong resolvent limit of a family of momentum cutoff Hamiltonians H/sup N/. The relationship between the scattering theories corresponding to H/sup N/ and H/sub theta/ is examined.
Educational Use Research
Learning Resource Type Article
Publisher Date 1980-04-01
Publisher Department Department of Mathematics, The University of Alberta, Edmonton, Canada T6G 2G1
Publisher Place United States
Journal J. Math. Phys.
Volume Number 21
Issue Number 4
Organization Department of Mathematics, The University of Alberta, Edmonton, Canada T6G 2G1


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