On Schrödinger equation with square and inverse-square potentials

2024/04/06 by Atsuhide Ishida, Ishida, Atsuhide, Masaki Kawamoto +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Cold Atom Physics and Bose-Einstein Condensates #FOS: Mathematics #Quantum Mechanics and Non-Hermitian Physics

paper · pdf · doi:10.48550/arxiv.2404.04756

openalex publication_date 2024/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the linear and nonlinear Schrödinger equations with a time-decaying harmonic oscillator and inverse-square potential. This model retains a form of scale invariance, and using this property, we demonstrate the asymptotic completeness of wave operators and Strichartz estimates for linear propagators.

Cited by

• Inverse scattering for N-body time-decaying harmonic oscillators

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