Classical Solutions to a Linear Schrödinger Evolution Equation Involving a Coulomb Potential with a Moving Center of Mass

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概要

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• This paper is concerned with Cauchy problems for the linear Schrödinger evolution equation (i(∂/∂t) + Δ + |x – a(t)|–1 + V1(x,t))u(x,t) = f(x,t) in RN × [0,T], subject to initial condition: u(·,0) ∈ H2(RN) ∩ H2(RN), where i := $\sqrt{-1}$, N ≥ 3, T > 0 and a : [0,T] → RN expresses the center of the Coulomb potential, V1 and f are another real-valued potential and an inhomogeneous term, respectively, while H2(RN) := {v ∈ L2(RN); |x|2v ∈ L2(RN)}. We show that under some conditions on V1 and f the equation has a classical solution u(·) ∈ C1([0,T]; L2(RN)) ∩ C([0,T]; H2(RN) ∩ H2(RN)).

著者

• Yoshii Kentarou

  Science University of Tokyo

関連論文

• Classical Solutions to a Linear Schrödinger Evolution Equation Involving a Coulomb Potential with a Moving Center of Mass

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