MR2918149
Kentarou YOSHII
Kentarou YOSHII
Classical Solutions to a Linear Schrödinger Evolution Equation Involving a Coulomb Potential with a Moving Center of Mass
Funkcialaj Ekvacioj. Serio Internacia
54
2011
485--493
http://fe.math.kobe-u.ac.jp/FE/FullPapers/54-3/54_485.pdf
http://www.ams.org/mathscinet-getitem?mr=MR2918149
This paper is concerned with Cauchy problems for the linear Schrödinger evolution equation $(i(\partial/\partial t)+\Delta+|x-a(t)|^{-1}+V_1(x,t))u(x,t)=f(x,t)$ in $\mathbb{R}^N \times[0,T]$, subject to initial condition: $u(\cdot,0)\in H^2(\mathbb{R}^N)\cap H_2(\mathbb{R}^N)$, where $i :=\sqrt{-1}$, $N\ge 3$, $T>0$ and $a: [0,T]\to\mathbb{R}^N$ expresses the center of the Coulomb potential, $V_1$ and $f$ are another real-valued potential and an inhomogeneous term, respectively, while $H_2(\mathbb{R}^N) :=\{v\in L^2(\mathbb{R}^N); |x|^2 v\in L^2(\mathbb{R}^N)\}$. We show that under some conditions on $V_1$ and $f$ the equation has a classical solution $u(\cdot)\in C^1([0,T];L^2(\mathbb{R}^N))\cap C([0,T];H^2(\mathbb{R}^N)\cap H_2(\mathbb{R}^N))$.
Schrödinger equation, Coulomb potential with a moving center of mass, Potentials singular at infinity, Existence and uniqueness of classical solutions, Energy estimates.
35Q41, 35A09.
54-485
2011
Classical Solutions to a Linear Schrödinger Evolution Equation Involving a Coulomb Potential with a Moving Center of Mass
Kentarou YOSHII
Kentarou YOSHII
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