Strichartz estimates for Schr\"{o}dinger operators with square potential with time-dependent coefficients

TL;DR

This paper extends Strichartz estimates for Schrödinger operators to more general time-dependent coefficients, including magnetic fields, removing previous restrictions and broadening applicability in quantum mechanics analysis.

Contribution

It removes previous assumptions on coefficients in Strichartz estimates for time-decaying harmonic oscillators and proves similar results for magnetic fields.

Findings

Strichartz estimates now hold for more general time-dependent coefficients.

Established estimates for Schrödinger operators with magnetic fields.

Broadened the class of potentials for which dispersive estimates are valid.

Abstract

Strichartz estimates for a time-decaying harmonic oscillator were proven with some assumptions of coefficients for the time-decaying harmonic potentials. The main results of this paper are to remove these assumptions and to enable us to deal with the more general coefficient functions. Moreover, we also prove similar estimates for time-decaying homogeneous magnetic fields.