Semiclassical quantification of some two degree of freedom potentials: A differential Galois approach
DOI10.1063/5.0169069arXiv2307.09318MaRDI QIDQ6188549
J. Tomás Lázaro, Chara Pantazi, Primitivo Belén Acosta-Humánez, Juan J. Morales-Ruiz
Publication date: 7 February 2024
Published in: Journal of Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2307.09318
Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain (34M50)
Cites Work
- Picard-Vessiot theory and integrability
- On the integrability of polynomial vector fields in the plane by means of Picard-Vessiot theory
- Galoisian approach to integrability of Schrödinger equation
- Non-integrability of some Hamiltonians with rational potentials
- An algorithm for solving second order linear homogeneous differential equations
- The semiclassical expansion
- Galoisian obstructions to integrability of Hamiltonian systems. I.
- Non-integrability criteria for Hamiltonians in the case of Lamé normal variational equations
- Rational KdV potentials and differential Galois theory
- Liouvillian propagators, Riccati equation and differential Galois theory
- A differential Galois approach to path integrals
- Discrete symmetric dynamical systems at the main resonances with application to axi-symmetric galaxies
- Nonintegrability of the Armbruster--Guckenheimer--Kim Quartic Hamiltonian Through Morales--Ramis Theory
- Liouvillian Propagators and Degenerate Parametric Amplification with Time-Dependent Pump Amplitude and Phase
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: Semiclassical quantification of some two degree of freedom potentials: A differential Galois approach