In this paper we introduce a class of semiclassical Fourier integral operators with global complex phases approximating the fundamental solutions (propagators) for time-dependent Schrödinger equations. Our construction is elementary, it is inspired by the joint work of the first author with Yu. Safarov and D. Vasiliev. We consider several simple but basic examples.
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Лаптев et al. (2000) studied this question.
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