ON THE PROBLEM OF THE RIGHT HAMILTONIAN UNDER SINGULAR FORM-SUM PERTURBATIONS

DOI10.1142/S0129055X00000022zbMath0974.47012MaRDI QIDQ4519829

Sergio A. Albeverio, Volodymyr Koshmanenko

Publication date: 4 December 2000

Published in: Reviews in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

perturbation of selfadjoint operatorsconvergence of regularized perturbationsKLMN-conditionsingular form-sum perturbations

Mathematics Subject Classification ID

Applications of operator theory in the physical sciences (47N50) Perturbation theory of linear operators (47A55) Linear symmetric and selfadjoint operators (unbounded) (47B25) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10)

Related Items (5)

Wedge-local quantum fields and noncommutative Minkowski space ⋮ Singular perturbations with an infinite constant coupling ⋮ Singularly perturbed Hamiltonians of a quantum Rayleigh gas defined as quadratic forms ⋮ On negative eigenvalues of generalized Laplace operators. ⋮ On Schrödinger operators perturbed by fractal potentials

Cites Work

• Removing cut-offs from singular perturbations: An abstract result
• Toward the rank-one singular perturbation theory of self-adjoint operators
• Regularization and convergence for singular perturbations
• A canonical decomposition for quadratic forms with applications to monotone convergence theorems
• Singular rank one perturbations of self-adjoint operators and Krein theory of self-adjoint extensions
• Rank one perturbations with infinitesimal coupling
• On form-sum approximations of singularly perturbed positive self-adjoint operators
• On the Right Hamiltonian for Singular Perturbations: General Theory
• TOWARDS THE RIGHT HAMILTONIAN FOR SINGULAR PERTURBATIONS VIA REGULARIZATION AND EXTENSION THEORY
• Square Powers of Singularly Perturbed Operators
• Singular perturbations of selfadjoint operators
• Perturbations of the Schrödinger equation by potentials with small support

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