On the scaling properties of the energy spectrum of hydrogen in a uniform magnetic field

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Abstract
The magnetic-field scaling relation between the coordinates, momenta and the energy in the Hamiltonian for the Kepler motion in a uniform magnetic field, i.e. H( gamma -13/p, gamma 23/r; gamma 13/m, gamma =1)= gamma -23/H(p,r; m, gamma ), where gamma =B/B0 is the normalised field strength and m the constant value of the angular moment,um B-parallel component is shown to ensure a representation of the semiclassical energy spectrum: E=(n+1/2)-2f( gamma 13/(n+1/2), gamma 13/m), m=0, +or-1, ...; n=0, 1, .... The authors discuss how the function f, in the two-dimensional approximation (z=pz=0, z//B), can be constructed.