A Study of the Lippmann-Schwinger Equation and Spectra for Some Unbounded Quantum Potentials

Christopher Winfield CSUCI, USA

We study the modified Lippmann-Schwinger Equation for certain model potentials V defined on ℝ^{3}, not of Rollnik class, and solutions to the equation in a weak sense. Further, we study the resolvent and the spectrum of the operator H = −Δ +cV in our model for non-zero constants c. In particular, we find that for sufficiently small c > 0, H has no singular spectrum.