WAVE OPERATOR-THEORY OF QUANTUM DYNAMICS

An energy-dependent wave operator theory of quantum dynamics is derive d for time-independent and time-dependent Hamiltonians. Relationships between Green's functions, wave operators, and effective Hamiltonians are investigated. Analytical properties of these quantities are especi ally relevant for studying resonances. A derivation of the relationshi p between the Green's functions and the (t,t') method of Peskin and Mo iseyev [J. Chem. Phys. 99, 4590 (1993)] is presented. The observable q uantities can be derived from the wave operators determined with the u se of efficient iterative procedures. As in the theory of Bloch operat ors for bound states, the theory is based on a partition of the full H ilbert space into three subspaces: the model space, an intermediate sp ace, and the outer space. On the basis of this partition an alternativ e definition of active spaces currently considered in large scale calc ulations is suggested. A numerical illustration is presented for sever al model systems and for the Stark effect in the hydrogen atom.