Quasiclassics and spectra for the $N$-particle Schr"odinger equation.
"Math. Notes 70, No.1, 132-136; translation from Mat. Zametki
70, No.1, 146-149 (2001).
Semiclassical techniques including WKB and Maslov methods|
|81Q05||Closed and approximate solutions to the Schroedinger, Dirac, Klein-Gordon and other quantum-mechanical equations|
|82-01||Instructional exposition textbooks, tutorial papers, etc.|
An interesting re-derivation and partial improvement of the
Bogolyubov's asymptotic construction of spectra for a class of
Schroedinger equations where the number of particles tends to
infinity. In contrast to the 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 ansatzs for the two-body interaction potential as well
as for the wave functions in their phase-amplitude form.
81Q05; 82-01; 82-08
multiparticle system; statistical limit; eigenvalues and eigenfunctions;
asymptotic solution; Bogolyubov method