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arXiv · 2204.00954

Quantum quasi-Lie systems: properties and applications

J. F. Cariñena·J. de Lucas·C. Sardón
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Abstract

A Lie system is a non-autonomous system of ordinary differential equations describing the integral curves of a $t$-dependent vector field taking values in a finite-dimensional Lie algebra of vector fields. Lie systems have been generalised in the literature to deal with $t$-dependent Schr\"odinger equations determined by a particular class of $t$-dependent Hamiltonian operators, the quantum Lie systems, and other differential equations through the so-called quasi-Lie schemes. This work extends quasi-Lie schemes and quantum Lie systems to cope with $t$-dependent Schr\"odinger 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.

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J. F. Cariñena, J. de Lucas, C. Sardón. 2022-04-02. Quantum quasi-Lie systems: properties and applications. https://doi.org/10.1140/epjp%2Fs13360-023-03883-9

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