On self-adjoint extensions and symmetries in quantum mechanics

DOI10.1007/s00023-014-0379-4zbMath1456.81179arXiv1402.5537OpenAlexW2041986890MaRDI QIDQ498601

Alberto Ibort, Fernando Lledó, Juan Manuel Pérez-Pardo

Publication date: 29 September 2015

Published in: Annales Henri Poincaré (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.5537

Mathematics Subject Classification ID

Linear symmetric and selfadjoint operators (unbounded) (47B25) Applications of Lie groups to the sciences; explicit representations (22E70) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Unitary representations of locally compact groups (22D10)

Related Items (10)

Quantum magnetic billiards: boundary conditions and gauge transformations ⋮ Hyperspherical \(\delta\)-\(\delta'\) potentials ⋮ Quantum controllability on graph-like manifolds through magnetic potentials and boundary conditions ⋮ Moving walls and geometric phases ⋮ Dirac-like operators on the Hilbert space of differential forms on manifolds with boundaries ⋮ Self-adjoint extensions and unitary operators on the boundary ⋮ Finite element method to solve the spectral problem for arbitrary self-adjoint extensions of the Laplace-Beltrami operator on manifolds with a boundary ⋮ Representation of non-semibounded quadratic forms and orthogonal additivity ⋮ Fundamental solutions for the wave operator on static Lorentzian manifolds with timelike boundary ⋮ Field fluctuations and Casimir energy of 1D-fermions

Cites Work

• On periodic matrix-valued Weyl--Titchmarsh functions
• Self-adjoint extensions in quantum mechanics. General theory and applications to Schrödinger and Dirac equations with singular potentials.
• Positivity of Wightman functionals and the existence of local nets
• Unbounded elements affiliated with \(C^*\)-algebras and non-compact quantum groups
• Manifolds, tensor analysis, and applications.
• Operator theory in the \(C^*\)-algebra framework
• Perturbation theory for linear operators.
• One cannot hear orbifold isotropy type
• On the dense point and absolutely continuous spectrum for Hamiltonians with concentric \(\delta\) shells
• Self-adjoint extensions of the Laplace-Beltrami operator and unitaries at the boundary
• Reduction theory for unbounded closed operators in Hilbert space
• On unitary ray representations of continuous groups
• Numerical Solutions of the Spectral Problem for Arbitrary Self-Adjoint Extensions of the One-Dimensional Schrödinger Equation
• Spectral Theory and Quantum Mechanics
• Self-adjoint extensions of restrictions
• Projective covering group versus representation groups
• Dirac Hamiltonian with Coulomb potential and spherically symmetric shell contact interactiona)
• On the projective unitary representations of connected Lie groups
• Casimir effect and global theory of boundary conditions
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