2018/05/08 by Vladimir Kalitvianski, Kalitvianski, Vladimir
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #General Physics (physics.gen-ph) #Quantum and Classical Electrodynamics #Quantum chaos and dynamical systems #physics.gen-ph
paper · pdf · doi:10.48550/arxiv.1805.03021
Original study, 40 pages, 59 figures, text slightly improved
openalex publication_date 2018/05/08 · arxiv created 2018/05/29 · arxiv updated 2018/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
I study some possibilities of analytically solving a particular Sturm-Liouville problem with step-wise (piece-constant) coefficients with help of an iterative procedure mentioned in my previous paper (Green's function sum rules). I construct short, simple, but very accurate analytical formulae for calculating the ground state eigenvalue and eigenfunction as well as for calculating the first eigenfunction. I study numerical precision of the obtained approximations together with the perturbation theory results.