The evolution operator of the Hartree-type equation with a quadratic potential

DOI10.1088/0305-4470/37/16/005zbMath1051.35060arXivmath-ph/0312004OpenAlexW3098062264MaRDI QIDQ4812481

A. Yu. Trifonov, Aleksandr L. Lisok, Alexander Shapovalov

Publication date: 23 August 2004

Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0312004

zbMATH Keywords

Cauchy problemexact solutionssymmetry operatorsMaslov complex germ

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs in connection with quantum mechanics (35Q40) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory (81Q70)

Related Items (6)

The nonlinear Schrödinger equation for a multi-dimensional system in an oscillator field ⋮ Semiclassical spectral series of a Hartree-type operator corresponding to a rest point of the classical Hamilton-ehrenfest system ⋮ Semiclassical propagation of coherent states for the Hartree equation ⋮ A semiclassical approximation for the nonstationary two-dimensional nonlinear Schrödinger equation with an external field in polar coordinates ⋮ Quasi-energy spectral series for a nonlocal Gross-Pitaevskii equation ⋮ Multiphase semiclassical approximation of an electron in a one-dimensional crystalline lattice. III: From ab initio models to WKB for Schrödinger-Poisson

This page was built for publication: The evolution operator of the Hartree-type equation with a quadratic potential