Simplicity of extremal eigenvalues of the Klein-Gordon equation

Details Simplicity of extremal eigenvalues of the Klein-Gordon equation Simplicity of extremal eigenvalues of the Klein-Gordon equation

2010-08-14

arxiv.org/abs/1008.2469v1

Physics

Mathematical Physics

Scientific paper

We consider the spectral problem associated with the Klein-Gordon equation for unbounded electric potentials. If the spectrum of this problem is contained in two disjoint real intervals and the two inner boundary points are eigenvalues, we show that these extremal eigenvalues are simple and possess strictly positive eigenfunctions. Examples of electric potentials satisfying these assumptions are given.

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