Semilinear Schrödinger evolution equations with inverse-square and harmonic potentials via pseudo-conformal symmetry

Toshiyuki Suzuki

doi:10.3934/cpaa.2021163

Article Contents

2021, Volume 20, Issue 12: 4347-4377. Doi: 10.3934/cpaa.2021163

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Semilinear Schrödinger evolution equations with inverse-square and harmonic potentials via pseudo-conformal symmetry

Toshiyuki Suzuki

Department of Mathematics, Faculty of Engineering, Kanagawa University, 3-27-1 Rokkakubashi, Kanagawa-ku, Yokohama city, Kanagawa, JAPAN

Received: April 30, 2021

Revised: July 31, 2021

Early access: September 2021

Published: December 2021

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Abstract

We consider the Cauchy problems for Schrödinger equations with an inverse-square potential and a harmonic one. Since the Mehler type formulas are completed, the pseudo-conformal transforms can be constructed. Thus we can convert the problems into the nonautonomous Schrödinger equations without a harmonic oscillator.

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Mathematics Subject Classification: Primary: 35Q55, 35Q40; Secondary: 81Q15.

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