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

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

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Veröffentlicht in:	Journal of mathematical physics 2024-07, Vol.65 (7)
Hauptverfasser:	Kato, Keiichi, Nakahashi, Wataru, Tadano, Yukihide
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Sprache:	eng
Schlagworte:	Schrodinger equation Smoothness
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container_title	Journal of mathematical physics
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creator	Kato, Keiichi Nakahashi, Wataru Tadano, Yukihide
description	We study non-smoothness of the fundamental solution for the Schrödinger equation with a spherically symmetric and super-quadratic potential in the sense that V(x) ≥ C\|x\|2+ɛ at infinity with constants C > 0 and ɛ > 0. More precisely, we show the fundamental solution E(t, x, y) does not belong to C1 as a function of (t, x, y), which partially solves Yajima’s conjecture.
doi_str_mv	10.1063/5.0184443
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subjects	Schrodinger equation Smoothness
title	Non-smoothness of the fundamental solutions for Schrödinger equations with super-quadratic and spherically symmetric potential
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