Abstract
Effective Schrödinger equations, governing the mean movement of a system influenced by fast oscillating external perturbation, are derived. The method represents a direct and straightforward quantum extension of the Kapitza’s approach provided in the Schrödinger picture. First-order terms (over inverse frequency of external driving) in effective Hamiltonians that cannot be eliminated by a unitary transformation, have been derived. Additional terms, in comparison with a standard equation, are similar to those found in the classical case and they may be responsible for a variety of new interesting effects.
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