Algebraic theory of the dynamical Stark-Zeeman effect for hydrogenlike atoms

The problem of calculating the time-evolution operator within a given n shell for a hydrogenlike atom located in nonstationary electric and magnetic fields has been studied. Using the Fock SO(4) group reduces this to a set of problems with a time-dependent Hamiltonian that can be written as a linear combination of operators which span a finite-dimensional Lie algebra. Alternative methods of evolution-operator parametrization, through a product-of-exponents procedure (the Wei-Norman method) and by means of D functions based on Euler angles and Cayley-Klein parameters, are discussed. It is shown that the evolution-operator calculation can be reduced to the investigation of a pair of two-level systems. The approach developed here is applied to the problem of evolution of a hydrogen atom in constant and harmonic electric fields. Analytical solutions obtained within the frame of standard perturbation theory, in the resonance and adiabatic approximations, and for the case of quasidegeneracy are given.