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Products of projections and self-adjoint operators
(Elsevier Science Inc, 2018-10)
Let H be a Hilbert space and L(H) be the algebra of all bounded linear operators from H to H. Our goal in this article is to study the set P⋅Lh of operators in L(H) that can be factorized as the product of an orthogonal ...
The time-dependent Schrödinger equation: the need for the Hamiltonian to be self-adjoint
(Sociedade Brasileira de Física, 2008)
We present some simple arguments to show that quantum mechanics operators are required to be self-adjoint. We emphasize that the very definition of a self-adjoint operator includes the prescription of a certain domain of ...
CONSTRUCTING QUANTUM OBSERVABLES AND SELF-ADJOINT EXTENSIONS OF SYMMETRIC OPERATORS. III. SELF-ADJOINT BOUNDARY CONDITIONS
(SPRINGER, 2008)
This paper completes the review of the theory of self-adjoint extensions of symmetric operators for physicists as a basis for constructing quantum-mechanical observables. It contains a comparative presentation of the ...
Self-adjointness of two-dimensional Dirac operators on corner domains
(European Matjermatical, 2021)
We investigate the self-adjointness of the two-dimensional Dirac operator D, with quantum-dot and Lorentz-scalar delta-shell boundary conditions, on piecewise C-2 domains (with finitely many corners). For both models, we ...
Self-adjoint operators on inner product spaces over fields of power series
(WALTER DE GRUYTER GMBH, 2008)
Theorems on orthogonal decompositions are a cornerstone in the classical theory of real (or complex) matrices and operators on R-n. In the paper we consider finite dimensional inner product spaces (E,Phi) over a field K = ...
On eigenvalue accumulation for non-self-adjoint magnetic operators
(ELSEVIER SCIENCE BV, 2017)
In this work, we use regularized determinants to study the discrete spectrum generated by relatively compact non-self-adjoint perturbations of the magnetic Schrodinger operator (-i del - A)(2) -b in R-3, with constant ...
Spectral functions of non-essentially self-adjoint operators
(IOP Publishing, 2012-09)
One of the many problems to which Dowker devoted his attention is the effect of a conical singularity in the base manifold on the behavior of the quantum fields. In particular, he studied the small-t asymptotic expansion ...
Hamiltonian self-adjoint extensions for(2+1)-dimensional Dirac particles
(IOP Publishing, 2001-12)
We study the stationary problem of a charged Dirac particle in (2+1) dimensions in the presence of a uniform magnetic field B and a singular magnetic tube of flux Phi = 2 pi kappa/e. The rotational invariance of this ...
Self-adjointness of two-dimensional dirac operators on domains
(2017)
We consider Dirac operators defined on planar domains. For a large class of boundary conditions, we give a direct proof of their self-adjointness in the Sobolev space H-1.