https://doi.org/10.1140/epjp/s13360-023-03883-9
Regular Article
Quantum quasi-Lie systems: properties and applications
1
Department of Theoretical Physics and IUMA, University of Zaragoza, c. Pedro Cerbuna 12, 50009, Zaragoza, Spain
2
Department of Mathematical Methods in Physics, University of Warsaw, ul. Pasteura 5, 02-093, Warsaw, Poland
3
Department of Applied Mathematics, Polytechnic University of Madrid (UPM), c. José Gutiérrez Abascal 2, 28006, Madrid, Spain
Received:
3
December
2022
Accepted:
9
March
2023
Published online:
18
April
2023
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.
Contribution to the Focus Point on “Mathematics and Physics at the Quantum-Classical Interface” edited by D.I. Bondar, I. Joseph, G. Marmo, C. Tronci.
© The Author(s) 2023
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