DOI: 10.1017/s0305004100035283. Lower-bound energies and the Virial theorem in wave mechanics

Lower-bound energies and the Virial theorem in wave mechanics

10.1017/s0305004100035283

Crossref journal-article

Cambridge University Press (CUP)

Mathematical Proceedings of the Cambridge Philosophical Society (56)

Abstract

ABSTRACTSeveral forms of the lower-bound variational method for the calculation of the eigenvalues in a wave-mechanical problem are considered, and compared; the particular case of the harmonic oscillator being chosen. All forms have certain unsatisfactory features, but some of them are considerably worse than others. One reason why calculations of lower bounds are in general less satisfactory than Ritz-type calculations of an upper bound is shown to be that whereas, in the presence of a scale factor, this latter wave-function satisfies the virial theorem, in none of the lower-bound wave-functions is this true. Similar calculations are reported for the ground state of the helium atom.

Bibliography

Caldow, G. L., & Coulson, C. A. (1961). Lower-bound energies and the Virial theorem in wave mechanics. Mathematical Proceedings of the Cambridge Philosophical Society, 57(2), 341â347.

Authors 2

G. L. Caldow (first)
C. A. Coulson (additional)

References 12 Referenced 26

10.1073/pnas.45.6.850
{'key': 'S0305004100035283_ref012', 'article-title': '855', 'volume': '63', 'author': 'Fock', 'year': '1930', 'journal-title': 'Z. Phys'} / Z. Phys / 855 by Fock (1930)
10.1098/rspa.1928.0098
10.1143/JPSJ.4.334
{'key': 'S0305004100035283_ref004', 'article-title': '199', 'volume': '53', 'author': 'Stevenson', 'year': '1938', 'journal-title': 'Phys. Rev'} / Phys. Rev / 199 by Stevenson (1938)
10.1103/PhysRev.54.375
{'key': 'S0305004100035283_ref006', 'volume-title': 'Variational methods for eigenvalue problems', 'author': 'Gould', 'year': '1957'} / Variational methods for eigenvalue problems by Gould (1957)
10.1103/PhysRev.115.366
{'key': 'S0305004100035283_ref010', 'first-page': '229', 'volume-title': 'Quantum chemistry', 'author': 'Kauzmann', 'year': '1957'} / Quantum chemistry by Kauzmann (1957)
10.1039/tf9454100141
10.1073/pnas.20.9.529
10.1103/PhysRev.105.1490

Dates

Type	When
Created	16 years, 9 months ago (Nov. 7, 2008, 10:43 a.m.)
Deposited	6 years, 2 months ago (June 4, 2019, 4:31 p.m.)
Indexed	1 month, 3 weeks ago (July 1, 2025, 9:31 a.m.)
Issued	64 years, 4 months ago (April 1, 1961)
Published	64 years, 4 months ago (April 1, 1961)
Published Online	16 years, 9 months ago (Oct. 24, 2008)
Published Print	64 years, 4 months ago (April 1, 1961)

Funders 0

None

BibTeX

@article{Caldow_1961, title={Lower-bound energies and the Virial theorem in wave mechanics}, volume={57}, ISSN={1469-8064}, url={http://dx.doi.org/10.1017/s0305004100035283}, DOI={10.1017/s0305004100035283}, number={2}, journal={Mathematical Proceedings of the Cambridge Philosophical Society}, publisher={Cambridge University Press (CUP)}, author={Caldow, G. L. and Coulson, C. A.}, year={1961}, month=apr, pages={341–347} }

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