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The trace of the generalized harmonic oscillator

Jared Wunsch (1999)

Annales de l'institut Fourier

We study a geometric generalization of the time-dependent Schrödinger equation for the harmonic oscillator D t + 1 2 Δ + V ψ = 0 ( 0 . 1 ) where Δ is the Laplace-Beltrami operator with respect to a “scattering metric” on a compact manifold M with boundary (the class of scattering metrics is a generalization of asymptotically Euclidean metrics on n , radially compactified to the ball) and V is a perturbation of 1 2 ω 2 x - 2 , with x a boundary defining function for M (e.g. x = 1 / r in the compactified Euclidean case). Using the quadratic-scattering...

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