On a heavy quantum particle. (English) Zbl 1417.81129
Summary: We consider the Schrödinger equation for a particle on a flat \(n\)-torus with a bounded potential depending on time. The mass of the particle equals \(1/\mu^2\), where \(\mu\) is a small parameter. We show that the Sobolev \(H^\nu\)-norms of the wave function grow approximately as \(t^\nu\) on the time interval \(t\in[-t_\ast, t_\ast]\), where \(t_\ast\) is slightly less than \(O(1/\mu)\).
MSC:
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
| 81Q35 | Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices |
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
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