Zentralblatt MATH

"Kucherenko, V.V."
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).
[ISSN 0001-4346]
Primary classification:
81Q20 Semiclassical techniques including WKB and Maslov methods
Secondary classification:
81Q05Closed and approximate solutions to the Schroedinger, Dirac, Klein-Gordon and other quantum-mechanical equations
82-01Instructional exposition textbooks, tutorial papers, etc.
82-08Computational methods

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 "81Q20"

keywords multiparticle system; statistical limit; eigenvalues and eigenfunctions; asymptotic solution; Bogolyubov method