Quantum versus Classical Mechanics and Integrability Problems

DOI10.1007/978-3-030-18379-0zbMath1435.81005OpenAlexW4241452632MaRDI QIDQ5380625

Maciej Błaszak

Publication date: 6 June 2019

Full work available at URL: https://doi.org/10.1007/978-3-030-18379-0

zbMATH Keywords

integrable systemsquantizationseparable systems

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to quantum theory (81-02) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Geometry and quantization, symplectic methods (81S10) Deformation quantization, star products (53D55) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Geometric quantization (53D50) Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory (37-02) Special quantum systems, such as solvable systems (81Q80) Hamiltonian and Lagrangian mechanics (70Hxx) Canonical quantization (81S08)

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Systematic construction of nonautonomous Hamiltonian equations of Painlevé type. I. Frobenius integrability ⋮ Systematic construction of nonautonomous Hamiltonian equations of Painlevé‐type. II. Isomonodromic Lax representation ⋮ Systematic construction of non‐autonomous Hamiltonian equations of Painlevé‐type. III. Quantization ⋮ Miura maps for Stäckel systems ⋮ The continuity equation in the phase space quantum mechanics

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