β Scribed by John D Dollard; Charles N Friedman
No coin nor oath required. For personal study only.
For free and interacting Hamiltonians, Ho and H = H,, + V(r) acting in L2(R3, dx) with V(r) a radial potential satisfying certain technical conditions, and for 9) a real function on R with v' > 0 except on a discrete set, we prove that the Moller wave operators Q* = strong limit eiWHJ e-ifVtHo) t-?*LQ exist and are independent of v. The scattering operator s = (Q+)*Qis shown to be unitary. Our proof utilizes time independent methods (eigenfunction expansions) and is effective in cases not previously analyzed, e.g. V(r) = sin r/r and many others.
π SIMILAR VOLUMES
The exact complexity of the weak pigeonhole principle is an old and fundamental problem in proof complexity. Using a diagonalization argument, J. B. Paris et al. (J. Symbolic Logic 53 (1988), 1235-1244) showed how to prove the weak pigeonhole principle with bounded-depth, quasipolynomialsize proofs.
We present a new proof of the well known theorem on the existence of signed (integral) t-designs due to Wilson and Graver and Jurkat.