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Approximation of a point perturbation on a Riemannian manifold. (English. Russian original) Zbl 1176.81052
Theor. Math. Phys. 158, No. 1, 40-47 (2009); translation from Teor. Mat. Fiz. 158, No. 1, 49-57 (2009).
Summary: We show that the Hamiltonian of point interaction on a Riemannian manifold with bounded geometry can be obtained as a limit (in the sense of uniform resolvent convergence) of a sequence of scaling Hamiltonians with short-range interaction.

MSC:
81Q35 Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
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