Year: 2023
Type: article
Abstract: A Lie system is a non-autonomous system of ordinary differential equations describing the integral curves of a t-dependent vector field that is equivalent to a t-dependent family of vector fields within a finite-dimensional Lie algebra of vector fields. Lie systems have been generalised in the literature to deal with t-dependent Schrödinger equations determined by a particular class of t-dependent Hamiltonian operators, the quantum Lie systems, and other systems of differential equations through the so-called quasi-Lie schemes. This work extends quasi-Lie schemes and quantum Lie systems to cope with t-dependent Schrödinger equations associated with the here-called quantum quasi-Lie systems. To illustrate our methods, we propose and study a quantum analogue of the classical nonlinear oscillator searched by Perelomov, and we analyse a quantum one-dimensional fluid in a trapping potential along with quantum t-dependent Smorodinsky–Winternitz oscillators.
Authors: J.F. Cariñena, J. de Lucas, C. Sardón
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,590
Awards: G490073602, G927431303
OpenAlex ID: W4366279904