Considering singular Sturm--Liouville differential expressions of the type \[ \tau_{\alpha} = -(d/dx)x^{\alpha}(d/dx) + q(x), \quad x \in (0,b), \; \alpha \mathbb{R}, \] we employ some Sturm comparison-type results in spirit Kurss to derive criteria for $\tau_{\alpha}$ be limit point and circle case at $x=0$. More precisely, if $\alpha \mathbb{R}$ $0 0$ such that $0<x$ sufficiently small, \begi...

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...

In the present paper, we consider a 2 ? block operator matrices with unbounded entry operators acting on Banach spaces. Under some conditions, develop criteria for its self-adjointness and closedness. The obtained results are applied to an Hamiltonian matrix.

The possibility of composite systems arising out of a point charge interacting with a Nielsen-Olesen vortex in 2+1-dimensions is investigated. It is shown that classical bounded orbits are possible for certain ranges of parameters. Long lived metastable states are shown to exist, in a semi-classical approach, from the study of the effective potential. Loss of self-adjointness of the Hamiltonian...

Spectra of the second derivative operators corresponding to the special PT -symmetric point interactions are studied. The results are partly the completion of those obtained in [1]. The particular PT -symmetric point interactions causing unusual spectral effects are investigated for the systems defined on a finite interval as well. The spectrum of this type of interactions is very far from the ...

In this work we explore the self-adjointness of the GUP-modified momentum and Hamiltonian operators over different domains. In particular, we utilize the theorem by von-Newmann for symmetric operators in order to determine whether the momentum and Hamiltonian operators are self-adjoint or not, or they have self-adjoint extensions over the given domain. In addition, a simple example of the Hamil...