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A Geometric Approach to Time Evolution Operators of Lie Quantum Systems

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Abstract

Lie systems in Quantum Mechanics are studied from a geometric point of view. In particular, we develop methods to obtain time evolution operators of time-dependent Schrödinger equations of Lie type and we show how these methods explain certain ad hoc methods used in previous papers in order to obtain exact solutions. Finally, several instances of time-dependent quadratic Hamiltonian are solved.

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Authors and Affiliations

  1. Departamento de Física Teórica, Universidad de Zaragoza, 50009, Zaragoza, Spain

    José F. Cariñena & Javier de Lucas

  2. Departamento de Análisis Económico, Universidad de Zaragoza, 50005, Zaragoza, Spain

    Arturo Ramos

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  1. José F. Cariñena
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  2. Javier de Lucas
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  3. Arturo Ramos
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Correspondence to José F. Cariñena.

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Cariñena, J.F., de Lucas, J. & Ramos, A. A Geometric Approach to Time Evolution Operators of Lie Quantum Systems. Int J Theor Phys 48, 1379–1404 (2009). https://doi.org/10.1007/s10773-008-9909-5

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