95-444 Lev Kapitanski and Igor Rodnianski

Regulated smoothing for Schr\"odinger evolution (35K, AMSTeX) Oct 3, 95

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Abstract. We study the smoothing of solutions of time-dependent multidimensional Schr\"odinger equations with growing at infinity potentials. We show that if the potential grows slower than quadratically, then the faster the initial condition $\psi(0,x)$ decays at infinity the more regular the wavefunction $\psi(t,x)$ is for $t>0$. In particular, the fundamental solution is infinitely differentiable for $t>0$. We also prove analogous results for the Schr\"odinger equation with magnetic field.

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