Accurate Eigenenergies for the Magnetized Hydrogen Atom

Abstract

The year of 1986 was extremely fruitful in results for the quadratic Zeeman effect. We mention three examples: first, quasi-Landau resonances having a closer spacing than 1.5 Kω near the zero-energy threshold have been reported experimentally by the Bielefeld group^1,2 and explained theoretically.^3–6 The second example is the investigations connected with the manifestation of quantum chaos, i.e. how does classical deterministic chaos manifest itself in the quantum spectrum of energies.^4,7,8 Connected with this is the very interesting work of Wintgen⁹ showing the existence of long-range correlations in the quantum spectrum. These contributions are particularly interesting because in contrast to previous studies of model Hamiltonians, they are based on a real physical system which can be investigated in the laboratory. As observed by Professor Friedrich in his lecture at this Conference, the magnetized hydrogen atom is becoming the system par excellence to investigate quantum chaos. The third example is the beautiful results of O’Mahony and Taylor on the quadratic Zeeman effect for nonhydrogenic systems.^10,11 The central point in almost all the aforementioned theoretical works was the calculation of the energy spectrum of a magnetized atom.