Transition amplitude methods for quantum processes in low-frequency fields

There has been a growing interest in the effects of intense electromagnetic fields on the process of detachment from bound states. The nature of a bound state depends on the specifics of an experiment. There is a large variety of objects in these experiments. Among these are atoms, molecules, elementary particles, and solid state structures subjected to an intense electromagnetic wave. In spite of the variety of these experiments, they are all based on the same phenomenon of detachment from a bound state in an external field less than the internal force produced by the binding potential. This is entirely a quantum phenomenon because it is absolutely impossible to remove a classical particle from a potential well by a field that cannot lift the particle above the barrier confining the particle in the well. The experiments stimulated growth of theoretical research in quantum processes involving strong electromagnetic waves. The most consistent and universal method, called strong-field approximation, has been developed within the last few decades. This method was used for a variety of phenomena in a wide range of intensities and frequencies and it gave good agreement with experiments. For low frequencies, however, the probability of the detachment obtained from the strong-field approximation does not match some experiments accurately enough even though the shape of the spectral distribution for these probabilities matches the experiments quite well. This dissertation addresses this issue and suggests a method to correct the strong-field approximation for the low frequency domain. This method gives the correct probability for the entire spectrum and explains the meaning of this spectrum as well as its relation to the time dependence of the electromagnetic field.