TITLE:
Building Wave Functions of the Outer Electron for Alkaline Atoms Theory and Wave Functions Representation
AUTHORS:
Amaury de Kertanguy
KEYWORDS:
Polarization Potential, Experimental Quantum Defects, Quantum Wave Functions, Mathematica Software
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.8 No.11,
November
27,
2020
ABSTRACT: The effects of the polarization potential serve to model spectra of alkaline atoms. These effects have been known for a long time and notably explained by the physicist Max Born (1926). The experimental knowledge of these alkaline spectra enables us to specify the values of these quantum defects. A simple code is used to calculate two quantum defects for which δl can be distinguished as: δs l = 0 and δp l = 1. On the theoretical part, it is possible to have an analytical expression for these quantum defects δl. A second code gives the correct wave functions modified by the quantum defects δl with the condition for the principal number: n* = n –δl ≥ 1. It is well known that δl → 0 when the kinetic momentum l ≥ 4, and for such momenta the spectra turns out to be hydrogenic. Modern software such as Mathematica, allows us to efficiently generate the polynomes defining wave functions with fractional quantum numbers. This leads to a good theoretical representation of these wave functions. To get numerically the quantum defects, a simple code is given to obtain these quantities when the levels assigned to a transition are known. Then, the quantum defects are inserted into the arguments of the correct modified wave functions for the outer electron of an atom or ion undergoing the short range polarization potential.