Quantum dynamics of a spin-1/2 charged particle in the presence of magnetic field with scalar and vector couplings

The quantum dynamics of a spin-1/2 charged particle in the presence of magnetic field is analyzed for the general case where scalar and vector couplings are considered. The energy spectra are explicitly computed for different physical situations, as well as their dependencies on the magnetic field strength, spin projection parameter and vector and scalar coupling constants.Comment: arXiv admin note: text overlap with arXiv:1403.411

On dB spaces with nondensely defined multiplication operator and the existence of zero-free functions

In this work we consider de Branges spaces where the multiplication operator by the independent variable is not densely defined. First, we study the canonical selfadjoint extensions of the multiplication operator as a family of rank-one perturbations from the viewpoint of the theory of de Branges spaces. Then, on the basis of the obtained results, we provide new necessary and sufficient conditions for a real, zero-free function to lie in a de Branges space.Comment: 13 pages, no fugures. Theorem and remark have been added, typographical erros correcte