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A Laplace operator with boundary conditions singular at one point

Marco Marlettta ; Grigori Rozenblioum (Institutionen för matematiska vetenskaper, matematik)
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL (1751-8113). Vol. 42 (2009), 12,
[Artikel, refereegranskad vetenskaplig]

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.



Denna post skapades 2010-08-20. Senast ändrad 2011-01-03.
CPL Pubid: 124958

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Fysik
Matematisk fysik

Chalmers infrastruktur