QUADRATIC ZEEMAN EFFECT IN HYDROGEN RYDBERG STATES - RIGOROUS BOUND-STATE ERROR-ESTIMATES IN THE WEAK-FIELD REGIME

Applying a method based on some results due to Kato [Proc. Phys. Soc. Jpn. 4, 334 (1949)], we show that series of Rydberg eigenvalues and Rydberg eigenfunctions of hydrogen in a uniform magnetic field can be calculated with a rigorous error estimate. The efficiency of the method decreases as the eigenvalue density increases and as gamman3 --> 1, where gamma is the magnetic-field strength in units of 2.35 X 10(9) G and n is the principal quantum number of the unperturbed hydrogenic manifold from which the diamagnetic Rydberg states evolve. Fixing gamma at the laboratory value 2 X 10(-5) and confining our calculations to the region gamman3 < 1(weak-field regime), we obtain extremely accurate results up to states corresponding to the n = 32 manifold.