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...

We introduce here a generalization of the modified Bernstein polynomials for Jacobi weights using the q-Bernstein basis proposed by G.M. Phillips to generalize classical Bernstein Polynomials. The function is evaluated at points which are in geometric progression in ]0, 1[. Numerous properties of the modified Bernstein Polynomials are extended to their q-analogues: simultaneous approximation, p...

The quantization of closed cosmologies makes it necessary to study squared Dirac operators on closed intervals and the corresponding quantum amplitudes. This paper shows that the proof of essential self-adjointness of these second-order elliptic operators is related to Weyl’s limit point criterion, and to the properties of continuous potentials which are positive near zero and are bounded on th...

It is widely appreciated that the iterative solution of linear systems of equations with large sparse matrices is much easier when the matrix is symmetric. It is equally advantageous to employ symmetric iterative methods when a nonsymmetric matrix is self-adjoint in a non-standard inner product. Here, general conditions for such self-adjointness are considered. In particular, a number of known ...