Semiclassical Asymptotics of the Spectrum of the Hydrogen Atom in an Electromagnetic Field Near the Upper Boundaries of Spectral Clusters

Semiclassical Asymptotics of the Spectrum of the Hydrogen Atom in an Electromagnetic Field Near the Lower Boundaries of Spectral Clusters

“…Since, as shown in [6], the number − e 2 1 a (17a+15) determines the lower boundaries of spectral clusters, we look for ξ near the lower boundaries in the form…”

“…It is of interest to consider the states of the system corresponding to the boundaries of spectral clusters where the Lagrange submanifolds almost collapse and it is impossible to represent the solutions over them. Based on the method proposed in [3,5], it was proved in [6] that, near the upper boundaries of spectral clusters, there is a series of eigenvalues of the operator (1.1) admitting the asymptotics…”