[PDF]    https://doi.org/10.3952/physics.v57i2.3513

Open access article / Atviros prieigos straipsnis

Lith. J. Phys. 57, 66–77 (2017)


NEW POSSIBILITIES OF HARMONIC OSCILLATOR BASIS APPLICATION FOR CALCULATION OF THE GROUND STATE ENERGY OF A COULOMB NON-IDENTICAL THREE-PARTICLE SYSTEM
Algirdas Deveikis
Vytautas Magnus University, Vileikos 8, LT-44404, Kaunas, Lithuania
E-mail: algirdas.deveikis@vdu.lt

Received 21 December 2016; revised 23 February 2017; accepted 16 March 2017

A new harmonic oscillator (HO) expansion method for calculation of the non-relativistic ground state energy of the Coulomb non-identical three-particle systems is presented. The HO expansion basis with different size parameters in the Jacobi coordinates instead of only one unique oscillator length parameter in the traditional treatment is introduced. This method is applied to calculate the ground state energy of a number of Coulomb three-particle systems for up to 28 excitation HO quanta. The obtained results suggest that the HO basis with different size parameters in the Jacobi coordinates could lead to significant increasing of the rate of convergence for the ground state energy
than in the traditional approach.
Keywords: harmonic oscillator basis, ground state energy, three-particle systems, quantum systems with
Coulomb potential
PACS: 03.65.Ge, 31.15.-p, 36.10.-k

NAUJOS HARMONINIO OSCILIATORIAUS BAZĖS TAIKYMO GALIMYBĖS, SKAIČIUOJANT KULONINĖS TRIJŲ NETAPATINGŲ DALELIŲ SISTEMOS PAGRINDINĖS BŪSENOS ENERGIJĄ

Algirdas Deveikis
Vytauto Didžiojo universitetas, Kaunas, Lietuva

Pasiūlytas naujas harmoninio osciliatoriaus (HO) bazės taikymo metodas skaičiuojant kuloninės trijų netapatingų dalelių sistemos nereliatyvistinę pagrindinės būsenos energiją. Skirtingai nei tradiciniuose HO bazės taikymuose, naudojančiuose tik vieną variacinį osciliatorinį parametrą, įvesti skirtingi variaciniai parametrai kiekvienai vidinei Jakobi koordinatei. Pateikto metodo veiksmingumas pademonstruotas apskaičiuojant eilės trijų netapatingų dalelių sistemų pagrindinių būsenų energijas iki 28 HO sužadinimo kvantų skaičiaus. Rezultatai palyginami su įvertinimais, gautais naudojant tradicinę HO bazę, ir kitų autorių duomenimis. Matome žymų siūlomo metodo privalumą, palyginti su tradicinio HO bazės taikymo galimybėmis, skaičiuojant kuloninių trijų netapatingų dalelių sistemų nereliatyvistines pagrindinių būsenų energijas.

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