A Laplace operator with boundary conditions singular at one point
Artikel i vetenskaplig tidskrift, 2009

We discuss a recent paper of Berry and Dennis (J. Phys. A: Math. Theor. 2008 41 135203) concerning a Laplace operator on a smooth domain with singular boundary condition. We explain a paradox in the article (J. Phys. A: Math. Theor. 2008 41 135203) and show that if a certain additional condition is imposed, the result is a spectral problem for a self-adjoint operator having only eigenvalues and no continuous spectrum. The eigenvalues accumulate at ±∞ only, and we obtain the asymptotic behaviours of the counting functions n+(λ) and n−(λ) for positive and negative eigenvalues. The physical meaning of the additional boundary condition is not yet clear.


Marco Marlettta

Cardiff University

Grigori Rozenblioum

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Journal of Physics A: Mathematical and Theoretical

1751-8113 (ISSN) 1751-8121 (eISSN)

Vol. 42



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