A Geometric Approach to Time Evolution Operators of Lie Quantum Systems

被引：9
|
作者：
Carinena, Jose F. [1 ]
de Lucas, Javier [1 ]
Ramos, Arturo [2 ]
机构：
[1] Univ Zaragoza, Dept Fis Teor, E-50009 Zaragoza, Spain
[2] Univ Zaragoza, Dept Anal Econ, Zaragoza 50005, Spain
来源：
INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS | 2009年 / 48卷 / 05期
关键词：
Time evolution; Lie systems; DEPENDENT HARMONIC-OSCILLATOR; SUPERPOSITION FORMULAS; DIFFERENTIAL-EQUATIONS; SCHRODINGER-EQUATION; RICCATI EQUATION; WAVE-FUNCTION; PHASE; PARTICLE; MOTION; STATES;
D O I：
10.1007/s10773-008-9909-5
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
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 Schrodinger 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.
引用
收藏
页码：1379 / 1404
页数：26
相关论文
共 50 条
  • [21] Evolution equation for geometric quantum correlation measures
    Hu, Ming-Liang
    Fan, Heng
    PHYSICAL REVIEW A, 2015, 91 (05):
  • [22] Geometric magnetism in open quantum systems
    Campisi, Michele
    Denisov, Sergey
    Haenggi, Peter
    PHYSICAL REVIEW A, 2012, 86 (03):
  • [23] Lie algebraic approach to quantum driven optomechanics
    Paredes-Juarez, A.
    Ramos-Prieto, I
    Berrondo, M.
    Recamier, J.
    PHYSICA SCRIPTA, 2020, 95 (03)
  • [24] Characteristic time operators as quantum clocks
    Farrales, Ralph Adrian E.
    Galapon, Eric A.
    PHYSICS LETTERS A, 2025, 532
  • [25] Time evolution and the Schrodinger equation on time dependent quantum graphs
    Smilansky, Uzy
    Sofer, Gilad
    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2024, 57 (06)
  • [26] Effective Theory of Nonadiabatic Quantum Evolution Based on the Quantum Geometric Tensor
    Bleu, O.
    Malpuech, G.
    Gao, Y.
    Solnyshkov, D. D.
    PHYSICAL REVIEW LETTERS, 2018, 121 (02)
  • [27] THE PHASE-SPACE APPROACH TO TIME EVOLUTION OF QUANTUM STATES IN CONFINED SYSTEMS: THE SPECTRAL SPLIT-OPERATOR METHOD
    Kolaczek, Damian
    Spisak, Bartlomiej J.
    Woloszyn, Maciej
    INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS AND COMPUTER SCIENCE, 2019, 29 (03) : 439 - 451
  • [28] Functional Integrals in Geometric Approach to Quantum Theory
    Frolov, Igor
    Schwarz, Albert
    UNIVERSE, 2023, 9 (05)
  • [29] GENERAL SOLUTIONS OF QUANTUM MECHANICAL EQUATIONS OF MOTION WITH TIME-DEPENDENT HAMILTONIANS: A LIE ALGEBRAIC APPROACH
    Kuna, Maciej
    Naudts, Jan
    REPORTS ON MATHEMATICAL PHYSICS, 2010, 65 (01) : 77 - 108
  • [30] Dissipative time evolution of observables in non-equilibrium statistical quantum systems
    Nachbagauer H.
    The European Physical Journal C - Particles and Fields, 1999, 8 (1) : 171 - 182
12345