This article is cited in 2 papers

Solution of the operator equation $i\varepsilon dy/dt=A(t)y$ on intervals containing turning points

E. A. Grinina

V. A. Fock Institute of Physics, Saint-Petersburg State University

Abstract: We obtain formal solutions of the equation $i\varepsilon dy/dt=A(t)y$ in the form of complete asymptotic expansions as $\varepsilon\to0$ on intervals containing parabolic or hyperbolic turning points. The highest orders of the power series in $\varepsilon$ for the formal solutions are studied in detail.

Received: 15.04.1999
Revised: 16.09.1999

DOI: 10.4213/tmf572

 English version: Theoretical and Mathematical Physics, 2000, 122:3, 298–311

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