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Finding gaps in a spectrum

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.
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https://hal.archives-ouvertes.fr/hal-00157479
Contributor : Amaury Mouchet <>
Submitted on : Tuesday, June 26, 2007 - 12:00:22 PM
Last modification on : Thursday, February 7, 2019 - 4:50:11 PM
Document(s) archivé(s) le : Thursday, April 8, 2010 - 6:28:30 PM

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  • HAL Id : hal-00157479, version 1
  • ARXIV : 0706.3800

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Hector Giacomini, Amaury Mouchet. Finding gaps in a spectrum. Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2007, 40 (39), pp.F921-F928. ⟨hal-00157479⟩

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