Abstract:
An integral representation of classical $S$-matrix for one-dimensional non-linear
non-stationary problem is rigorously deduced, which is valid for all values of quantum
numbers, including small ones. Comparison of the quasi classical results with the
exact ones for the model of oscillator with the external forces, makes it possible to
estimate the error of the method of classical $S$-matrix and its uniform Eiry approximation.
Possibilities of constructing new “uniform” approximations, which could be
useful in many-dimensional problems of atomic collisions, are discussed.
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