2014/10/21 by Paolo Amore, Amore, Paolo, Francisco M. Fernández +1
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #Quantum, superfluid, helium dynamics #Spectroscopy and Quantum Chemical Studies #math-ph #math.MP #quant-ph
paper · pdf · doi:10.48550/arxiv.1410.5813
arxiv created 2014/10/21 · openalex publication_date 2014/10/21 · arxiv updated 2014/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We generalize a recently proposed small-energy expansion for one-dimensional quantum-mechanical models. The original approach was devised to treat symmetric potentials and here we show how to extend it to non-symmetric ones. Present approach is based on matching the logarithmic derivatives for the left and right solutions to the Schrödinger equation at the origin (or any other point chosen conveniently) . As in the original method, each logarithmic derivative can be expanded in a small-energy series by straightforward perturbation theory. We test the new approach on four simple models, one of which is not exactly solvable. The perturbation expansion converges in all the illustrative examples so that one obtains the ground-state energy with an accuracy determined by the number of available perturbation corrections.