Wave front set for solutions to Schrödinger equations with long-range perturbed harmonic oscillators |
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| Authors: | Shikuan Mao |
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| Affiliation: | 1. School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China;2. Graduate School of Mathematical Sciences, University of Tokyo, Tokyo 153-8914, Japan |
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| Abstract: | In this paper we consider a Schrödinger operator with variable coefficients and harmonic potential. The perturbation is assumed to be long-range in a sense similar to the work of Nakamura (2009) [13]. We construct a modified propagator, and then by using this propagator and also the propagator of the unperturbed free harmonic oscillator we characterize the propagation of singularities for solutions to the equations. |
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| Keywords: | Microlocal singularities Wave front set Harmonic oscillator Schrö dinger equation Long-range perturbation |
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