Explicit summation of the constituent WKB series and new approximate wave functions
The independent solutions of the one-dimensional Schrödinger equation are approximated by means of the explicit summation of the leading constituent WKB series. The continuous matching of the particular solutions gives the uniformly valid analytical approximation to the wave functions. A detailed nu...
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| Format: | Article |
| Language: | English |
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Wiley
2002-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/S1110757X02112046 |
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| _version_ | 1832564952387289088 |
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| author | Vladimir V. Kudryashov Yulian V. Vanne |
| author_facet | Vladimir V. Kudryashov Yulian V. Vanne |
| author_sort | Vladimir V. Kudryashov |
| collection | DOAJ |
| description | The independent solutions of the one-dimensional Schrödinger equation are approximated by means of the explicit summation of the leading constituent WKB series. The continuous matching of the particular solutions gives the uniformly valid analytical approximation to the wave functions. A detailed numerical verification of the proposed approximation is performed for some exactly solvable problems arising from different kinds of potentials. |
| format | Article |
| id | doaj-art-48978b9384f1447492f918d2f4d186b0 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2002-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-48978b9384f1447492f918d2f4d186b02025-02-03T01:09:42ZengWileyJournal of Applied Mathematics1110-757X1687-00422002-01-012626527510.1155/S1110757X02112046Explicit summation of the constituent WKB series and new approximate wave functionsVladimir V. Kudryashov0Yulian V. Vanne1Institute of Physics, National Academy of Sciences of Belarus, 68 F. Skaryna Avenue, Minsk 220072, BelarusDepartment of Chemistry, University of Konstanz, Fach M721 D-78457, Konstanz, GermanyThe independent solutions of the one-dimensional Schrödinger equation are approximated by means of the explicit summation of the leading constituent WKB series. The continuous matching of the particular solutions gives the uniformly valid analytical approximation to the wave functions. A detailed numerical verification of the proposed approximation is performed for some exactly solvable problems arising from different kinds of potentials.http://dx.doi.org/10.1155/S1110757X02112046 |
| spellingShingle | Vladimir V. Kudryashov Yulian V. Vanne Explicit summation of the constituent WKB series and new approximate wave functions Journal of Applied Mathematics |
| title | Explicit summation of the constituent WKB series and new approximate wave functions |
| title_full | Explicit summation of the constituent WKB series and new approximate wave functions |
| title_fullStr | Explicit summation of the constituent WKB series and new approximate wave functions |
| title_full_unstemmed | Explicit summation of the constituent WKB series and new approximate wave functions |
| title_short | Explicit summation of the constituent WKB series and new approximate wave functions |
| title_sort | explicit summation of the constituent wkb series and new approximate wave functions |
| url | http://dx.doi.org/10.1155/S1110757X02112046 |
| work_keys_str_mv | AT vladimirvkudryashov explicitsummationoftheconstituentwkbseriesandnewapproximatewavefunctions AT yulianvvanne explicitsummationoftheconstituentwkbseriesandnewapproximatewavefunctions |