Abstract
A simple proof of the absence of resonances for Schrödinger operators in the semiclassical limit is given under a generalized scaling and nontrapping (or virial) condition. The method of local distortion due to Hunziker is employed and a pseudo-differential operator calculus is used to construct the parametrix. The result is primarily intended for applications to the shape resonance, but can be also applied to various models including Stark effect and periodic potentials.
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Dedicated to Professor Tosihusa Kimura on his 60th birthday.
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Nakamura, S. A note on the absence of resonances for Schrödinger operators. Lett Math Phys 16, 217–223 (1988). https://doi.org/10.1007/BF00398958
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DOI: https://doi.org/10.1007/BF00398958