No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Exact solution of the compressed hydrogen atom
6. J. L. Marin and S. A. Cruz, “ On the use of direct variational methods to study confined quantum systems,” Am. J. Phys. 59, 931–935 (1991).
7. J. L. Marin, R. Rosas, and A. Uribe, “ Analysis of asymmetric confined quantum systems by the direct variational method,” Am. J. Phys. 63, 460–463 (1995).
14. G. Bastard, Wave Mechanics Applied to Semiconductor Heterostructures (Les Ulis, Les Editions de Physique, 1988).
15. J. C. Stewart and K. D. Pyatt, Jr., “ Lowering the ionization potentials in plasmas,” Astrophys. J. 144, 1203–1211 (1966).
18. M. Abramowitz
and I. A. Stegun
, Handbook of Mathematical Functions
, New York
). The (free) online version of this book is at <http://dlmf.nist.gov
22. N. Aquino, G. Campoy, and H. E. Montgomery, Jr., “ Highly accurate solutions for the confined hydrogen atom,” Int. J. Quantum Chem. 107, 1548–1558 (2007).
23.Using a more precise mathematical terminology, the UHA wavefunction obeys a Neumann-type boundary condition, while the CHA wavefunction obeys a Dirichlet-type boundary condition.
24. L. Pauling and E. B. Wilson, Introduction to Quantum Mechanics (McGraw-Hill, New York, 1935).
25.This finding validates a conjecture formulated in Ref. 5, about the ordering of the CHA eigenvalues.
26. L. Brus, “ Electron-electron and electron-hole interactions in small semiconductor crystallites: The size dependence of the lowest excited electronic state,” J. Chem. Phys. 80(9), 4403–4409 (1984).
27.In order to pass from Eq. (8) to Eq. (10), it is enough to calculate a few bL values, using Eq. (9) and then keep only the linear contributions in β.
28. J. M. Ferreyra and C. R. Proetto, “ Strong confinement approach for impurities in quantum dots,” Phys. Rev. B 52, R2309–R2312 (1995);
28. C. R. Proetto, “ Comment on ‘Screening in Semiconductor Nanocrystallites and its Consequences for Porous Silicon,’” Phys. Rev. Lett. 76, 2824 (1996). Cin(x) refers to the Cosine integral function (Ref. 18, p. 231).
29.Defined as . The explicit expression is , as given in Ref. 24, p. 144.
30. L. Bányai and S. W. Koch, Semiconductor Quantum Dots (World Scientific, Singapore, 1993).
31. Y. Kayanuma, “ Quantum-size effects of interacting electrons and holes in semiconductor microcrystals with spherical shapes,” Phys. Rev. B 38, 9797–9805 (1988).
32.Within a given family, n = N + L and . Since , this implies that [see Eq. (16)], in agreement with the discussion above on the ordering of the energy levels in Fig. 1.
33. N. H. March and M. P. Tosi, “ Caged H atom and H2 molecule in relation to Monte Carlo study of molecular dissociation at constant volume”, Il Nuovo Cimento D, 18, 1061–1067 (1996).
37. R. G. Parr and W. Yang, Density-Functional Theory of Atoms and Molecules (Oxford U.P., New York, 1989).
38. R. M. Dreizler and E. K. U. Gross, Density Functional Theory (Springer, Berlin, 1990).
Article metrics loading...
Full text loading...
Most read this month