Semiclassical Theory of Shape Resonances in Quantum Mechanics

In this paper, we prove the existence of shape resonances in the semi-classical approximation for Hamiltonians of the form [italic]H([lowercase Greek]Lambda) [triple bar symbol] −([capital Greek]Delta + ([lowercase Greek]Lambda2[italic]V + [italic]U on [italic]L2([bold]R[superscript italic]n), where ([lowercase Greek]Lambda [triple bar symbol] 1/h[with stroke], h[with stroke] [triple bar symbol] (2[lowercase Greek]Pi)−1h.