Wave front set of solutions to Schr\"odinger equations with perturbed harmonic oscillators
Keiichi Kato, Shingo Ito
TL;DR
This paper characterizes the wave front sets of solutions to Schrödinger equations with harmonic oscillator potentials plus sub-quadratic perturbations, using wave packet transforms to analyze the evolution operator.
Contribution
It introduces a method to determine wave front sets for perturbed harmonic oscillator Schrödinger equations via wave packet transform representation.
Findings
Wave front sets are explicitly characterized for solutions.
The approach applies to sub-quadratic perturbations.
Provides a new analytical tool for Schrödinger equations.
Abstract
In this paper, we determine the wave front sets of solutions to Schr\"odinger equations of a harmonic oscillator with sub-quadratic perturbation by using the representation of the Schr\"odinger evolution operator of a harmonic oscillator via the wave packet transform.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Mathematical Analysis and Transform Methods · Spectral Theory in Mathematical Physics