This research will focus on three areas: 1) Stability and instability of quantum Hamiltonians with dense point and singular spectra; 2) Existence of absolutely continuous spectra of Schrodinger operators with random potential; and 3) Solutions of a commutator inequality which arose in connection with random Hamiltonians. This work is in the general area of mathematical physics. The problem examined by this researcher is to some extent a simple quantum analogue of the KAM problem in classical mechanics. Problems of this sort with time-periodic potentials are of considerable physical interest, particularly in connection with atoms in laser fields.
