On the Simplicity of the Eigenvalues of the Non-self-adjoint Mathieu-Hill Operators

O. A. Veliev

On the Simplicity of the Eigenvalues of the Non-self-adjoint Mathieu-Hill Operators

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arxiv 1301.1011 v2 pith:TJ73QPDW submitted 2013-01-06 math.SP

O. A. Veliev This is my paper · ORCID

classification math.SP

keywords eigenvaluesmathieu-hillnon-self-adjointantiperiodicboundaryconditionsdirichletfind

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We find conditions on the potential of the non-self-adjoint Mathieu-Hill operator such that the all eigenvalues of the periodic, antiperiodic, Dirichlet and Neumann boundary value problems are simple.

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By adding a gauge-singlet scalar to the Georgi-Machacek model and imposing classical scale invariance, the electroweak scale arises radiatively and the model predicts a scalon below 200 GeV and a heavier scalar below 600 GeV.

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