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1 LMPT - Laboratoire de Mathématiques et Physique Théorique 2 FRDP - Fédération de recherche Denis Poisson

Abstract : We propose a method for finding gaps in the spectrum of a differential operator. When applied to the one-dimensional Hamiltonian of the quartic oscillator, a simple algebraic algorithm is proposed that, step by step, separates with a remarkable precision all the energies even for a double-well configuration in a tunnelling regime. Our strategy may be refined and generalised to a large class of 1d-problems.

keyword : spectral problem spectral approximation gaps quartic oscillator

Author: Hector Giacomini - Amaury Mouchet -



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