The time evolution of an atom in constant magnetic fields is reduced to time evolution of the center of mass that does not depend directly on the magnetic field by the Born-Oppenheimer approximation.
The positions of resonances of systems of Schrödinger operators that are related to the mathemaical theory of molecular predissociation is determined as semiclassical asymptotics.
Propagation estimates are obtained for matrix-type Schrödinger operators related to molecular dynamics.
Finiteness of the number of critical values of the Hartree-Fock functional used in many-electron problems less than a constant smaller than the first energy threshold is proved.
For a critical value of the Hartree-Fock functional less than the first energy threshold it is proved that the set of all solutions to the Hartree-Fock equation associated with the critical value is a union of real-analytic subsets of a finite number of compact real-analytic manifolds.
A stationary definition of scattering matrices is given using asymptotic behaviors of generalized eigenfunctions, and it is proved that the definition is equivalent to the time-dependent definition in long-range N-body problems.
An a priori upper bound of local electronic densities in molecules defined by eigenfunctions is proved.