https://doi.org/10.1140/epjd/e2008-00176-1
Semiclassical method for calculating the energetic values of helium, lithium and beryllium atoms
National Institute for Laser, Plasma and Radiation
Physics, Laser Department, P.O. Box MG-36, 077125 Bucharest, Romania
Corresponding author: a ampopa@rdslink.ro
Received:
9
March
2008
Revised:
2
July
2008
Published online:
3
October
2008
In previous papers we have presented a wave model for
conservative bound systems resulted from the equivalency between
the Schrödinger and wave equations. We proved that the normal
curves of the characteristic surface of the wave equation, denoted
by C curves, are solutions of the Hamilton-Jacobi equation,
written for the same system, and correspond to the same constants
of motion as those resulting from the Schrödinger equation. In
this paper we present a method for computing the energetic values
of conservative bound systems which is based on the properties of
the C curves. The method is applied to the 
state of
helium, 
and 
states of lithium and 
state of beryllium. Our theoretical values are compared with
experimental data taken from well-known books. The relative error
of our method is less than 
.
PACS: 31.15.xg – Semiclassical methods / 02.40.Yy – Geometric mechanics / 41.20.-q – Applied classical electromagnetism
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2008
