The ''shake'' of a quantum system and the character of ''shake''-induced transitions

This paper treats the problem of basic characteristics of quantum transitions, stimulated by a sudden disturbance V(t). The proper ''shake'' theory for quantum systems is constructed by expanding the time-displacement operator S (t, t') in a power series in ωtau (hω is the typical eigenvalue of the unperturbed hamiltonian, tau is the characteristic collision time). If [V(t), V(t')]equals 0 at any Vtau/h, the ''shake'' theory gives a compact expression for the transition probabilities. Various atomic collision processes are discussed from the ''shake'' point of view. If an impulse deltap is transferred to the quantum system during the short time (ωtau << 11), the transition probabilities are determined by the value of universal parameter N approximately deltap. deltaR/h (uncertainty deltaR results from the slow motion of the unperturbed system)