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- W2079676588 abstract "A general method for treating highly singular perturbations V of self-adjoint operators H in Hilbert space is applied to the case of perturbations of (− iddx)n in L2 (R1 by (multiplications by) distributions. A self-adjoint operator HV that agrees with H + V in the usual sense when V is sufficiently regular, and is moreover a continuous function of V, within the class of distributions under consideration, in the strong operator topology for unbounded self-adjoint operators, is shown to exist. This operator HV need not be semi-bounded, or determined by a sesquilinear form associated with H + V. The method proceeds by construction of the corresponding unitary propagator in the interaction representation, essentially e−itHVeitH, which is shown to be expressible as a uniformly convergent perturbative series for small times." @default.
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- W2079676588 date "1980-08-01" @default.
- W2079676588 modified "2023-10-18" @default.
- W2079676588 title "Singular perturbations in the interaction representation" @default.
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- W2079676588 doi "https://doi.org/10.1016/0022-1236(80)90057-9" @default.
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