Asymptotics of solutions to the time-dependent Schrödinger equation with a small Planck constant. (Russian. English summary) Zbl 07812344
Zh. Vychisl. Mat. Mat. Fiz. 47, No. 10, 1746-1751 (2007); translation in Comput. Math. Math. Phys. 47, No. 10, 1675-1680 (2007).
Summary: A regularized asymptotics of the solution to the time-dependent Schrödinger equation in which the spatial derivative is multiplied by a small Planck constant is constructed. It is shown that the asymptotics of the solution contains a rapidly oscillating boundary layer function.
MSC:
| 35Q40 | PDEs in connection with quantum mechanics |
| 35B25 | Singular perturbations in context of PDEs |
Keywords:
singularly perturbed time-dependent Schrödinger equation; regularized asymptotics; solutionsReferences:
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