Asymptotics of hypergeometric coherent states and eigenfunctions of the hydrogen atom in a magnetic field. Determination of self-consistent energy levels

Theoretical and Mathematical Physics. 2025. Vol. 222. No. 3. P. 453–470.

A. V. Pereskokov

The spectral problem for the hydrogen atom in a magnetic field perturbed by a self-consistent field is
considered. An asymptotic expansion of self-consistent energy levels is obtained. An asymptotic expansion
of hypergeometric coherent states near the sphere |q| = 2 is found. The asymptotics of the norm of the
asymptotic eigenfunctions in the space L2(R3) is calculated.

Keywords: coherent transformation, когерентное преобразование, самосогласованное поле, self-consistent field, asymptotic eigenfunction, asymptotic eigenvalue, метод перевала, асимптотическое собственное значение, асимптотическая собственная функция, hypergeometric coherent states, saddle-point method, гипергеометрические когерентные состояния