Remark on wave front sets of solutions to Schrödinger equation of a free particle and a harmonic oscillator

In this paper, we determine the wave front sets of solutions to the Schrödinger equations of the Schrödinger evolution operator of a free particle and of a harmonic oscillator by using the representation of the Schrödinger evolution operator of a free particle introduced by Kato, Kobayashi and Ito (2011) and a new representation of the evolution operator of a harmonic oscillator via wave packet transform (short time Fourier transform). AMS 2010 Mathematics Subject Classification. 35Q41, 35A18.