Searcharxiv⌕ Search

arXiv subjects

V. Jakubsky

Publications and source records attributed to V. Jakubsky.

6 recordsLinked to original sources
arXiv2018

Two-dimensional Dirac fermion in presence of an asymmetric vector potential

We introduce the new, exactly solvable model of the two-dimensional Dirac fermion in presence of an asymmetric, Pöschl-Teller-like vector potential. Utilizing the translation invariance of the system, the effective one-dimensional stationary equation is brought into the form of the Heun equation and its fundamental solutions are found as an irreducible combination of two Gauss hypergeometric functions. The energy spectrum and the scattering is studied in dependence on the conserved longitudinal momentum as well as on the strength of the coupling.

hep-th↗
arXiv2006

A Positive-Definite Scalar Product for Free Proca Particle

We implement recent results of pseudo-Hermitian quantum mechanics to description of relativistic massive particle with spin-one. We derive a one-parameter family of Lorentz invariant positive-definite scalar products on the space of solutions of Proca equation.

hep-th↗
arXiv2005

Comment on `Solution of the Dirac equation for the Woods-Saxon potential with spin and pseudospin symmetry' [J. Y. Guo and Z-Q. Sheng, Phys. Lett. A 338 (2005) 90]

Out of the four bound-state solutions presented in loc. cit., only one (viz., the spin-symmetric one, in the low-mass regime) is shown compatible with the physical boundary conditions. We clarify the problem, correct the method and offer another, "missing" (viz., pseudospin-symmetric) new solution with certain counterintuitive "repulsion-generated" property.

math-ph↗
arXiv2005

PT-supersymmetric partner of a short-range square well

In a box of size $L$, a spatially antisymmetric square-well potential of a purely imaginary strength ${\rm i}g$ and size $l < L$ is interpreted as an initial element of the SUSY hierarchy of solvable Hamiltonians, the energies of which are all real for $g < g_c(l)$. The first partner potential is constructed in closed form and discussed.

quant-ph↗
arXiv2005

PT-symmetric supersymmetry in a solvable short-range model

The simplest purely imaginary and piecewise constant $\cal PT$-symmetric potential located inside a larger box is studied. Unless its strength exceeds a certain critical value, all the spectrum of its bound states remains real and discrete. We interpret such a model as an initial element of the generalized non-Hermitian Witten's hierarchy of solvable Hamiltonians and construct its first supersymmetric (SUSY) partner in closed form.

quant-ph↗