24 citations · 92 across the 19 of their papers we have counts for
4 papers · 1 filter
Ultrarelativistic (Cauchy) spectral problem in the infinite well
Elena V. Kirichenko, Piotr Garbaczewski, Vladimir Stephanovich +1
We analyze spectral properties of the ultrarelativistic (Cauchy) operator , provided its action is constrained exclusively to the interior of the interval $[-1,1] \subse…
Nonlocally-induced (fractional) bound states: Shape analysis in the infinite Cauchy well
Mariusz Żaba, Piotr Garbaczewski
Fractional (Lévy-type) operators are known to be spatially nonlocal. This becomes an issue if confronted with a priori imposed exterior Dirichlet boundary data. We address spectral…
Nonlocal random motions: The trapping problem
Piotr Garbaczewski, Mariusz Żaba
Lévy stable (jump-type) processes are examples of intrinsically nonlocal random motions. This property becomes a serious obstacle if one attempts to model conditions under which a…
Solving fractional Schroedinger-type spectral problems: Cauchy oscillator and Cauchy well
Mariusz Zaba, Piotr Garbaczewski
This paper is a direct offspring of Ref. [J. Math. Phys. 54, 072103, (2013)] where basic tenets of the nonlocally induced random and quantum dynamics were analyzed. A number of men…