NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2012, 3 (4), P. 9–19
HAMILTONIAN WITH ZERO-RANGE POTENTIALS HAVING INFINITE NUMBER OF EIGENVALUES
A.A.Boitsev – Saint Petersburg National Research University of Information Technologies, Mechanics and Optics, Saint Petersburg, Russia, student
I.Yu.Popov – Saint Petersburg National Research University of Information Technologies, Mechanics and Optics, Saint Petersburg, Russia, professor, D.Sc., popov1955@gmail.com
O.V.Sokolov – Saint Petersburg National Research University of Information Technologies, Mechanics and Optics, Saint Petersburg, Russia, student
Infinite chain of zero-range potentials having the Hamiltonian with infinite number of eigenvalues below the continuous spectrum is constructed. The model is based on the theory of self-adjoint extensions of symmetric operators.
Keywords: operator extensions theory, singular perturbation, point spectrum.
UDC 517.968
PACS 02.30.Tb, 42.25.Fx
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