Bateman's dual system revisited: quantization, geometric phase and relation with the ground-state energy of the linear harmonic oscillator

DOI10.1016/j.aop.2004.01.008zbMath1064.81064arXivquant-ph/0102128OpenAlexW1989523679MaRDI QIDQ1877775

Massimo Blasone, Petr Jizba

Publication date: 19 August 2004

Published in: Annals of Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/quant-ph/0102128

zbMATH Keywords

coherent statesgeometric phases1D harmonic oscillatorFeynman-Hibbs kernel formulaquantization of dissipative systems

Mathematics Subject Classification ID

Geometry and quantization, symplectic methods (81S10) Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory (81Q70)

Related Items (11)

Quantum damped oscillator. II: Bateman's Hamiltonian vs. 2D parabolic potential barrier ⋮ Quantum damped oscillator. I: Dissipation and resonances ⋮ On the quantization of the massive Bateman system ⋮ Dissipation and quantization for composite systems ⋮ Quantization of the damped harmonic oscillator revisited ⋮ Quantization and instability of the damped harmonic oscillator subject to a time-dependent force ⋮ Quantum dynamics of the damped harmonic oscillator ⋮ On the quantization of the massless Bateman system ⋮ Canonical quantization of so-called non-Lagrangian systems ⋮ QUANTIZATION OF NON-LAGRANGIAN SYSTEMS ⋮ A generalization of the Lagrange–Hamilton formalism with application to non-conservative systems and the quantum to classical transition

Cites Work

• Chaos in classical and quantum mechanics
• Dissipation and topologically massive gauge theories in the pseudo-Euclidean plane
• The Van Vleck formula, Maslov theory, and phase space geometry
• Quantization, group contraction and zero point energy
• Quantal phase factors accompanying adiabatic changes
• On Dissipative Systems and Related Variational Principles
• Squeezed states for general systems
• Particles and Sources
• On the Definition and Approximation of Feynman's Path Integrals
• Quantum theory: concepts and methods
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