Quasiclassical scattering of wave packets on a narrow band in which the potential rapidly changes
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.
scientific article; zbMATH DE number 4129335
scientific article