Non-smoothness of the fundamental solutions for Schrödinger equations with super-quadratic and spherically symmetric potential

2023/10/24 by Kato, Keiichi, Nakahashi, Wataru, Tadano, Yukihide
#35J10 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2310.15536

Abstract

We study non-smoothness of the fundamental solution for the Schrödinger equation with a spherically symmetric and super-quadratic potential in the sence that V(x)≥ C|x|^2+ε at infinity with constants C>0 and ε>0. More precisely, we show the fundamental solution E(t,x,y) does not belong to C¹ as a function of (t,x,y).

Related

• Short time asymptotics of the fundamental solutions for Schrödinger equations with non-smooth potentials
• Smoothness of the fundamental solution of Schrödinger equations with mild trapping
• A Fundamental Solution to the Schrödinger Equation with Doss Potentials and its Smoothness
• Solutions of the Schrödinger equation, boundary condition at the origin, and theory of distributions
• Fundamental solutions for Schrodinger operators with general inverse square potentials