Excited states in logarithmic perturbation theory
Teoretičeskaâ i matematičeskaâ fizika, Tome 68 (1986) no. 1, pp. 155-159
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It is generally assumed that in the logarithmic perturbation method the
magnitudes of the corrections to the logarithm of the unperturbed wave
function become infinite at the points at which the wave function has
zeros. Therefore, for excited states special devices, which greatly
complicate the calculation, have been proposed. It is shown in this
paper that in many cases the excited states can be calculated without
these complications by using the formulas for the ground state; the
corrections in this case remain finite at the zero points. A general
criterion for the existence of such cases is given. The need for special
devices is also eliminated for states for which the current is nonzero.
It is shown that the logarithmic perturbation method proposed by the
authors in an earlier study (1971) for excited states simplifies appreciably
in problems with a local perturbing potential.
@article{TMF_1986_68_1_a13,
author = {G. V. Vikhnina and V. S. Pekar},
title = {Excited states in logarithmic perturbation theory},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {155--159},
publisher = {mathdoc},
volume = {68},
number = {1},
year = {1986},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1986_68_1_a13/}
}
G. V. Vikhnina; V. S. Pekar. Excited states in logarithmic perturbation theory. Teoretičeskaâ i matematičeskaâ fizika, Tome 68 (1986) no. 1, pp. 155-159. http://geodesic.mathdoc.fr/item/TMF_1986_68_1_a13/