Two-dimensional quantisation of the quasi-Landau hydrogenic spectrum

Abstract

Based on the two-dimensional WKB model, an equation is derived from which the non-relativistic quasi-Landau energy spectrum of hydrogen-like atoms may be easily obtained. In addition, we discuss the solution of radial equations in the WKB approximation and its relation with models recently used to fit experimental data. The two-dimensional WKB model (Edmonds 1970, Starace 1973, Garstang 1977) has been very useful in the interpretation of experimental data concerning the quasi- Landau spectrum of hydrogen-like atoms. Although it is relatively crude, the success of the model is evident from work published in recent years (Fonck et a1 1978, 1980, Economou et a1 1978, Castro et a1 1980, Gay et a1 1980, Delande and Gay 1981a, b, Kara and McDowell 1981, Clark and Taylor 1980, 1982, Ferrante et a1 1982). The model consists basically of studying the complicated motion of a spinless particle of mass M in combined Coulomb and magnetic fields through the central potential