PERTURBATION OF SELF-ADJOINT OPERATORS BY DIRAC DISTRIBUTIONS

The existence of a family of self-adjoint Hamiltonians Hθ, θ∈ [0, 2ζ), corresponding to the formal expression H 0 + vδ(x) is shown for a general class of self-adjoint operators H0. Expressions for the Green's function and wavefunction corresponding to H0 are obtained in terms of the Green's function and wavefunction corresponding to H0. Similar results are shown for the perturbation of H0 by a finite sum of Dirac distributions. A prescription is given for obtaining Hθ as the strong resolvent limit of a family of momentum cutoff Hamiltonians H N. The relationship between the scattering theories corresponding to H N and Hθ is examined. © 1980 American Institute of Physics.