Russian Journal of Mathematical Physics

, Volume 26, Issue 1, pp 109–121 | Cite as

On a Heavy Quantum Particle

  • D. V. TreschevEmail author
  • O. E. ZubelevichEmail author


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/μ2, where μ is a small parameter. We show that the Sobolev Hν-norms of the wave function grow approximately as tν on the time interval t ∈ [−t*, t*], where t* is slightly less than O(1/μ).


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© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Lomonosov Moscow State UniversityMoscowRussia
  2. 2.Steklov Mathematical Institute of Russian Academy of SciencesMoscowRussia

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