an:06529374
Zbl 1332.34133
??aba, Mariusz; Garbaczewski, Piotr
Nonlocally induced (fractional) bound states: shape analysis in the infinite Cauchy well
EN
J. Math. Phys. 56, No. 12, 123502, 21 p. (2015).
00351358
2015
j
34L10 34A08 34B10 34D15 34L40
Summary: Fractional (L??vy-type) operators are known to be spatially nonlocal. This becomes an issue if confronted with \textit{a priori} imposed exterior Dirichlet boundary data. We address spectral properties of the prototype example of the Cauchy operator \((-\Delta)^{1/2}\) in the interval \(D = (-1, 1) \subset R\), with a focus on functional shapes of first few eigenfunctions and their fall-off at the boundary of \(D\). New high accuracy formulas are deduced for approximate eigenfunctions. We analyze how their shape reproduction fidelity is correlated with the evaluation finesse of the corresponding eigenvalues.{
\copyright 2015 American Institute of Physics}