Perturbation theory for short-range weakly-attractive potentials in one dimension

FERNÁNDEZ, FRANCISCO M.; AMORE, PAOLO

ANNALS OF PHYSICS (NEW YORK)

ACADEMIC PRESS INC ELSEVIER SCIENCE

Año: 2017 vol. 378 p. 253 - 263

0003-4916

We have obtained the perturbative expressions up to sixth order for the energy of the bound state in a one dimensional, arbitrarily weak, short range finite well, applying a method originally developed by Gat and Rosenstein Ref. [1]. The expressions up to fifth order reproduce the results already known in the literature, while the sixth order had not been calculated before. As an illustration of our formulas we have applied them to two exactly solvable problems and to a nontrivial problem.