Analytic approximate eigenvalues by a new technique. Application to sextic anharmonic potentials

5^th World Congress on Physics

July 17-18, 2018 Prague, Czech Republic

D. Diaz-Almeida and P. Martin

Universidad de Antofagasta, Chile
Universidad de Antofagasta, Chile

Posters & Accepted Abstracts: J Laser Opt Photonics

Abstract :

Harmonic potentials with sextic anharmonic terms play an important role in spectra of molecules such as ammonia and hydrogenbounded solids, and they might be considered as a potential model for quark confinement in Quantum Chromodynamics. Improvement in a recient technique denoted as multi-point quasi-rational approximants (MPQA), allowed us to obtain precise analytic approximations for the eigenvalues of the Schrödinger equation for every positive value of the perturbative parameter λ, using simultaneously power series and asymptotic expansions, as well as additional power series expansions around some intermediate points , 0 < < ∞. The present new technique uses rational approximants, as Pade´s method, but combined with other auxiliary functions as fractional powers, exponentials, trigonometricals, among others. The idea of the approximant is to build a function using rational functions together with auxiliary ones, as a bridge between Taylor and asymptotic expansions. Eigenvalues of sextic anharmonic potentials with the form ( ) = 2 + 6 were study. No general analytic solution to this problem is known. The accuracy of the analytic form here obtained is very good for every positive value of the parameter λ. The present analytic approximation is more elaborated than that for the quartic anharmonic potential, but its accuracy is about the same, and a similar number of terms has been also used. Its accuracy is high with a relative error less than 5 ∗ 10−3 using third degree polynomials. The higher the polynomial degree, the better the precision of the approximant. The highest relative errors are found for small values of λ

Biography :

E-mail: daniel.diaz@uantof.cl