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The Schrodinger operators with potentials p(x) which do not necessarily converge to a constant at infinity will be discussed. The potential p(x) = *i/|*|, x = (x\, x 2 ,--, x n ) G I^> * s an example. The radiation condition associated with such Schrόdinger operators is shown to have the form Vw -iyfk(vR)u = small at infinity, where R = R(x, λ) is a solution of the eikonal equation \VR\ 2 = 1 -p(x)/λ. This radiation condition is "nonspherical" in the sense that v^ is not proportional to the vector 3c = x/\x\ in general. The limiting absorption principle will be obtained using a priori estimates for the radiation condition.

The zero modes and zero resonances of the Dirac operatorWe shall show that every zero mode f (x) is continuous on R 3 and decays at infinity with the decay rate |x| −2 . Also, we shall show that H has no zero resonance if ρ > 3/2.

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