Abstract
The Mourre estimate is proved in the semiclassical limit for Schrödinger operators satisfying a nontrapping condition. Moreover, an abstract form of a theorem concerning the absence of resonances is given.
Similar content being viewed by others
References
Briet, P., Combes, J. M., and Duclos, P., On the location of resonances for Schrödinger operators in the simiclassical limit, I. Resonance free domains, J. Math. Anal. Appl. 126, 90–99 (1987).
Briet, P., Combes, J. M., and Duclos, P., Spectral properties of Schrödinger operators with trapping potentials in the semi-classical limit, in L. W., Knowels and Y., Saito (eds), Differential Equations and Mathematical Physics, Lecture Notes in Mathematics, Vol. 1285, Springer, Berlin, Heidelberg, New York, 1987, pp. 55–72.
Combes, J. M., Duclos, P., Klein, M., and Seiler, R., The shape resonance, Commun. Math. Phys. 110, 215–236 (1987).
Hislop, P. and Nakamura, S., Semiclassical resolvent estimates, Ann. Inst. H. Poincaré A51 (1989).
Hislop, P. and Sigal, I. M., Shape resonance in quantum mechanics, in L. W., Knowels and Y., Saito (eds), Differential Equations and Mathematical Physics, Lecture Notes in Mathematics, Vol. 1285, Springer, Berlin, Heidelberg, New York, 1987, pp. 180–196.
Hunziker, W., Distortion analyticity and molecular resonance curves, Ann. Inst. H. Poincaré, A45, 339–358 (1986).
Klein, M., On the absence of resonances for Schrödinger operators with non-trapping potentials in the classical limit, Commun. Math. Phys. 106, 485–494 (1986).
Nakamura, S., A note on the absence of resonances for Schrödinger operators, Lett. Math. Phys. 16, 217–223 (1988).
Sigal, I. M., Complex transformation method and resonances in one-body quantum systems, Ann. Inst. H. Poincaré, A41, 103–114, and Addendum A41, 333 (1984).
Sigal, I. M., Sharp bounds on resonance states and width of resonances, Adv. Appl. Math. 9, 127–166 (1988).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Graf, G.M. The Mourre estimate in the semiclassical limit. Lett Math Phys 20, 47–54 (1990). https://doi.org/10.1007/BF00417228
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00417228