Scaled energies and Fourier transforms

The form of the Hamiltonian for the atom in a strong magnetic field suggests a scaling transformation r = (7B)2/3r and p = (7B)-1/3p [564]. With this transformation, the EBK quantisation condition becomes 

Extra peaks in the Fourier transform spectrum have been found to correspond to many such orbits. Thus, a new understanding of the underlying classical dynamics has evolved. 

For large fields, the separation between Coulomb states becomes much smaller than the separation between quasi-Landau resonances, and one observes sequences of overlapping Rydberg channels distinguished by the 

Landau index 77, which overlap and interfere. There is a rich structure of interactions in the strong field problem as observations are extended into the continuum. The interested reader can consult a number of conference proceedings [438, 566, 567] and reviews [560, 568] for further details. 

The previous section concentrated on the one-electron problem, i.e. on the balance between the purely Coulombic and magnetic terms. As stressed continually throughout this book, the one-electron atom is an exceptional case, and there is also much to be learned by considering many-electron systems. 

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