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Quasiclassical scattering of wave packets on a narrow band in which the potential rapidly changes. (English. Russian original) Zbl 0689.35080

Math. Notes 45, No. 1-2, 72-77 (1989); translation from Mat. Zametki 45, No. 1, 106-114 (1989).
Let \(\psi\) satisfy an equation \[ i\hslash \partial \psi /\partial t=- \hslash^ 2\Delta \psi +| \nabla \Phi |^ 2V(\Phi (x)/\hslash)\psi +V_ 0(x)\psi,x\in {\mathbb{R}}, \] and an initial condition \[ H_{t=0}=\phi_ 0(x) \exp (i\hslash^{-1}S(x)), \] where functions \(\phi_ 0,S_ 0,\Phi,V_ 0\) and V are given. The asymptotics of \(\psi\) (x,t,\(\hslash)\) as \(\hslash \to 0\) and \(t\in [0,T]\) with fixed T is found.
Reviewer: D.R.Yafaev

MSC:

35Q99 Partial differential equations of mathematical physics and other areas of application
35B40 Asymptotic behavior of solutions to PDEs
35K15 Initial value problems for second-order parabolic equations
35P25 Scattering theory for PDEs
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References:

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