Accurate analytic approximations to eigenvalues anharmonic potentials x2+λx8
Precise analytic approximations have been found for the eigenvalues of the ground state in the anharmonic potentials x2+λx8. Rational functions combined with fractional powers are used to determine the new approximations. First, power series in the parameter has been found using an extension of the...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2020-03-01
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| Series: | Results in Physics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379719326270 |
| _version_ | 1818257312944488448 |
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| author | Pablo Martin Fernando Maass Daniel Diaz-Almeida |
| author_facet | Pablo Martin Fernando Maass Daniel Diaz-Almeida |
| author_sort | Pablo Martin |
| collection | DOAJ |
| description | Precise analytic approximations have been found for the eigenvalues of the ground state in the anharmonic potentials x2+λx8. Rational functions combined with fractional powers are used to determine the new approximations. First, power series in the parameter has been found using an extension of the quantum mechanics perturbation technique recently published. Modifications of these new technologies has been also developed to obtain asymptotic expansions in λ. The analytic functions here determined are just a bridge between both expansions. The maximum relative error of the best analytic approximation here determined is 0.006 (less than 1%). However, most of the relative errors for other values of λ, are smaller than 0.3%. Positive values of λ are only considered. |
| first_indexed | 2024-12-12T17:41:39Z |
| format | Article |
| id | doaj.art-1bb68c493d4f42c8827086a67d81500e |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-12-12T17:41:39Z |
| publishDate | 2020-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-1bb68c493d4f42c8827086a67d81500e2022-12-22T00:17:03ZengElsevierResults in Physics2211-37972020-03-0116102986Accurate analytic approximations to eigenvalues anharmonic potentials x2+λx8Pablo Martin0Fernando Maass1Daniel Diaz-Almeida2Departamento de Fisica, Universidad de Antofagasta, Av. Angamos 601, Antofagasta, Casilla, 170, 1240000, Chile; Corresponding author.Departamento de Fisica, Universidad de Antofagasta, Av. Angamos 601, Antofagasta, Casilla, 170, 1240000, ChileCentro de Desarrollo Energetico Antofagasta (CDEA), Universidad de Antofagasta, Av. Angamos 601, Antofagasta, Casilla, 170, 1240000, ChilePrecise analytic approximations have been found for the eigenvalues of the ground state in the anharmonic potentials x2+λx8. Rational functions combined with fractional powers are used to determine the new approximations. First, power series in the parameter has been found using an extension of the quantum mechanics perturbation technique recently published. Modifications of these new technologies has been also developed to obtain asymptotic expansions in λ. The analytic functions here determined are just a bridge between both expansions. The maximum relative error of the best analytic approximation here determined is 0.006 (less than 1%). However, most of the relative errors for other values of λ, are smaller than 0.3%. Positive values of λ are only considered.http://www.sciencedirect.com/science/article/pii/S221137971932627033C1041A2026A0626A99 |
| spellingShingle | Pablo Martin Fernando Maass Daniel Diaz-Almeida Accurate analytic approximations to eigenvalues anharmonic potentials x2+λx8 Results in Physics 33C10 41A20 26A06 26A99 |
| title | Accurate analytic approximations to eigenvalues anharmonic potentials x2+λx8 |
| title_full | Accurate analytic approximations to eigenvalues anharmonic potentials x2+λx8 |
| title_fullStr | Accurate analytic approximations to eigenvalues anharmonic potentials x2+λx8 |
| title_full_unstemmed | Accurate analytic approximations to eigenvalues anharmonic potentials x2+λx8 |
| title_short | Accurate analytic approximations to eigenvalues anharmonic potentials x2+λx8 |
| title_sort | accurate analytic approximations to eigenvalues anharmonic potentials x2 λx8 |
| topic | 33C10 41A20 26A06 26A99 |
| url | http://www.sciencedirect.com/science/article/pii/S2211379719326270 |
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