Quasiclassics and spectra for the \(N\)-particle Schrödinger equation (Q1566446)

An interesting re-derivation and partial improvement of Bogolyubov's asymptotic construction of spectra for a class of Schrödinger equations where the number of particles tends to infinity is given. In contrast to Bogolyubov's results, more freedom applies to the range of aggregated physical parameters (including mass), and only a few more terms appear in the innovated formulae. The key idea of the construction lies in the use of truncated Fourier-type ansatzes for the two-body interaction potential as well as for the wave functions in their phase-amplitude form.