We are focused on the idea that observables in quantum physics a bit more then just hermitian operators and this is, general, “tricky business”. The origin of comes from fact there is subtle difference between symmetric, hermitian, self-adjoint which immense importance formulating Quantum Mechanics. theory extensions presented through several physical examples some emphasis given implications a...

We investigate the self-adjointness of 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 prove existence a unique self-adjoint realization whose domain is included in Sobolev space $H^{1/2}$, formal form free operator. The main part our paper consists...

Institutions were introduced by Goguen and Burstall 8, 9, 10, 11] to formally capture the notion of logical system. Interpreting institutions as functors, and morphisms and representations of institutions as natural transformations, we give elegant proofs for the completeness of the categories of institutions with morphisms and representations, respectively, show that the duality between morphi...

We establish optimal order a priori error estimates for implicit– explicit BDF methods for abstract semilinear parabolic equations with timedependent operators in a complex Banach space setting, under a sharp condition on the non-self-adjointness of the linear operator. Our approach relies on the discrete maximal parabolic regularity of implicit BDF schemes for autonomous linear parabolic equat...

Examples of symmetric quantum semimartingales are easy to find, but essentially self-adjoint quantum semimartingales have, in general, proved elusive. This is not unexpected since a quantum semimartingale is in some sense an indefinite integral of a family of unbounded operators, and strong conditions are required to ensure that the sum of even two unbounded self-adjoint operators is self-adjoi...

We consider a Schrödinger operator with a magnetic field (and no electric field) on a domain in the Euclidean space with a compact boundary. We give sufficient conditions on the behavior of the magnetic field near the boundary which guarantees essential self-adjointness of this operator. From the physical point of view, it means that the quantum particle is confined in the domain by the magneti...

of N links joined at a single point. Each link supports a real locally integrable potential Vj ; the self–adjointness is ensured by the δ type boundary condition at the vertex. If all the links are semiinfinite and ideally coupled, the potential decays as x−1−ǫ along each of them, is non–repulsive in the mean and weak enough, the corresponding Schrödinger operator has a single negative eigenval...