Location of resonances generated by degenerate potential barrier

H. Baklouti, University of Sfax, Sfax, Tunisia
M. Mnif, University of Sfax, Sfax, Tunisia

E. J. Qualitative Theory of Diff. Equ., No. 18. (2006), pp. 1-11.

Abstract: We study resonances of the semi-classical Schr\"odinger operator $H = -h^2 \Delta + V$ on $L^2( \R^N)$. We consider the case where the potential $V$ have an absolute degenerate maximum. Then we prove that $H$ has resonances with energies $E = V_0 + e^{-i {\pi \over \sigma +1}} h^{ 2 \sigma \over \sigma +1} k_j + {\cal O}( h^{ 2 \sigma +1 \over \sigma +1} ),$ where $k_j $ is in the spectrum of some quartic oscillator.

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