Ground state eigenvalue of the anharmonic potential x4+λx6 by high accuracy analytic functions

• Published in: Results in physics 2020-09, Vol.18, p.103291, Article 103291
• Main Authors: Martin, Pablo, Diaz-Almeida, Daniel, Maass, Fernando
• Format: Article
• Language: English
• Subjects: 34A45; 34E05; 41A20; 41A60; 65L15; 81Q05; Anharmonic potentials; Approximations; Eigenvalues; MPQA
• ISSN: 2211-3797; 2211-3797
• DOI: 10.1016/j.rinp.2020.103291

•A new way of obtaining precise eigenvalues in Quantum Mechanics is presented.•The method use simultaneously perturbation theory around small and large values of a characteristic parameter λ.•Later a bridge approximations function is constructed through both expansions. High accuracy analytic functions have been determined for the ground state eigenvalue of the quantum anharmonic potential x4+λx6. The procedure here used is a new application of the multipoint quasi-rational approximation method (MPQA) to quantum mechanics. Previous applications of the technique were performed in the case where the eigenvalues of the potential were already known for the particular case of λ=0. The extension of the method, where this condition is not accomplished, is presented here. As a first step, power and asymptotic expansions have been now also determined. This is followed by the search of a bridge function connecting both expansions, and later the determination of the parameters. Accuracies smaller than 0.1% have been found with only nine parameters.