Demonstration of Systematic Improvements in Application of the Variational Method to Strongly Bound Potentials
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| Title: | Demonstration of Systematic Improvements in Application of the Variational Method to Strongly Bound Potentials |
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| Language: | English |
| Authors: | Ninemire, B., Mei, W. N. |
| Source: | International Journal of Mathematical Education in Science and Technology. Jul-Aug 2004 35(4):565-583. |
| Availability: | Customer Services for Taylor & Francis Group Journals, 325 Chestnut Street, Suite 800, Philadelphia, PA 19106. Tel: 800-354-1420 (Toll Free); Fax: 215-625-8914. |
| Peer Reviewed: | Y |
| Page Count: | 19 |
| Publication Date: | 2004 |
| Document Type: | Journal Articles Reports - Evaluative |
| Descriptors: | Item Response Theory |
| ISSN: | 0020-739X |
| Abstract: | In applying the variational method, six different sets of trial wave functions are used to calculate the ground state and first excited state energies of the strongly bound potentials, i.e. V(x)=x[2m], where m = 4, 5 and 6. It is shown that accurate results can be obtained from thorough analysis of the asymptotic behaviour of the solutions. Consequently, it was found that there is a progressive qualitative change in the wave functions from the harmonic to anharmonic and then strongly bounded region, which explains why using a harmonic oscillator wave function together with the conventional perturbative approach to calculate the energy correction, was unsuccessful. |
| Abstractor: | Author |
| Number of References: | 20 |
| Entry Date: | 2005 |
| Access URL: | https://taylorandfrancis.metapress.com/link.asp?target=contribution&id=K841033763730546 |
| Accession Number: | EJ691836 |
| Database: | ERIC |
| Abstract: | In applying the variational method, six different sets of trial wave functions are used to calculate the ground state and first excited state energies of the strongly bound potentials, i.e. V(x)=x[2m], where m = 4, 5 and 6. It is shown that accurate results can be obtained from thorough analysis of the asymptotic behaviour of the solutions. Consequently, it was found that there is a progressive qualitative change in the wave functions from the harmonic to anharmonic and then strongly bounded region, which explains why using a harmonic oscillator wave function together with the conventional perturbative approach to calculate the energy correction, was unsuccessful. |
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| ISSN: | 0020-739X |
