an:06358476
Zbl 1304.81069
??aba, Mariusz; Garbaczewski, Piotr
Solving fractional Schr??dinger-type spectral problems: Cauchy oscillator and Cauchy well
EN
J. Math. Phys. 55, No. 9, 092103, 20 p. (2014).
00337253
2014
j
81Q05 81Q10 35S05 35R11
nonl-ocal Schr??dinger operator; Cauchy oscillator; Cauchy well; spectral problems; Strang method
The authors present the results of a computer-assisted route to obtain the eigenvalues and the eigenfunctions of the \(1D\) Cauchy-Schr??dinger operator \(H=(-\Delta)^{1/2} + V\), \(V\) being a local potential. The Cauchy oscillator (which also has an analytical solution) and Cauchy finite well spectral problems are mainly envisaged. The algorithms employed are a non-local version of Strang's splitting method, which is based on Trotter product formula.
Mihai Pascu (Bucure??ti)
Zbl 1284.81012