Research PapersNo Access

Comment on the spherical quantum dot with interaction effects

Department of Chemistry, Technion - Israel Institute of Technology, Haifa 32000, Israel

https://doi.org/10.1142/S0217979217501156Cited by:0 (Source: Crossref)

Abstract

A series of studies of the lowest $^{3} P$ state of a model of a two-electron quantum dot, that consists of a finite spherical well [see, for example, Sivakami et al., Int. J. Mod. Phys. B24, 5561 (2010)], exhibited a range of interesting applications. However, the quantity of central interest, the expectation value of the interelectronic repulsion (that must be nonnegative) was calculated erroneously, yielding negative values. In the present note, this expectation value is evaluated with respect to the exact first-order perturbation theory wavefunction (the scheme considered in the papers cited above) as well as with respect to a minimal basis set Gaussian variational wavefunction. Reasonable agreement between the two schemes is confirmed, both yielding the expected positive values of the expectation value of the interelectronic repulsion, over the whole range of the relevant parameters.

Keywords:

PACS: 73.21.La, 03.65.Ge, 31.15.A

You currently do not have access to the full text article.
Recommend the journal to your library today!

References

1. B. Szafran, J. Adamowski and S. Bednarek, Physica E 4, 1 (1999). Crossref, ADS, Google Scholar
2. S. Bednarek, B. Szafran and J. Adamowski, Phys. Rev. B 59, 13036 (1999). Crossref, Web of Science, ADS, Google Scholar
3. A. R. Jeice and K. Navaneethakrishanan, Braz. J. Phys. 39, 526 (2009). Crossref, Web of Science, ADS, Google Scholar
4. A. Sivakami, A. R. Jeice and K. Navaneethakrishnan, Int. J. Mod. Phys. B 24, 5561 (2010). Link, Web of Science, ADS, Google Scholar
5. A. R. Jeice and K. S. J. Wilson, Indian J. Phys. 88, 1031 (2014). Crossref, Web of Science, ADS, Google Scholar
6. P. O. Löwdin, Advan. Chem. Phys. 2, 207 (1959). Web of Science, Google Scholar
7. E. U. Condon and G. H. Shortley, The Theory of Atomic Spectra (Cambridge University Press, Oxford, 1935). Google Scholar
8. J. C. Slater, Phys. Rev. 34, 1293 (1929). Crossref, ADS, Google Scholar
9. E. U. Condon and G. H. Shortley, Phys. Rev. 35, 1342 (1930). Crossref, ADS, Google Scholar
10. R. F. Bacher, Phys. Rev. 43, 264 (1933). Crossref, ADS, Google Scholar
11. G. Racah, Phys. Rev. 62, 438 (1943). Crossref, ADS, Google Scholar
12. G. H. Hardy, J. E. Littlewood and G. Pólya, Inequalities (Cambridge University Press, Oxford, 1967). Google Scholar
13. G. Katriel, personal communication (2016). Google Scholar
14. E. H. Lieb and B. Simon, Commun. Math. Phys. 53, 185 (1977). Crossref, Web of Science, ADS, Google Scholar
15. J. D. Morgan III and W. Kutzelnigg, J. Phys. Chem. 97, 2425 (1993). Crossref, Web of Science, Google Scholar
16. I. Shavitt, The Gaussian function in calculations of statistical mechanics and quantum mechanics, in Methods in Computational Physics, Vol. 2, eds. B. Alder, S. Fernbach and M. Rotenberg (Academic Press, New York, 1963), p. 1. Google Scholar