Equivalence of a harmonic oscillator to a free particle and Eisenhart lift
From MaRDI portal
Publication:2058645
DOI10.1016/j.aop.2021.168623zbMath1482.81008arXiv2106.09523OpenAlexW3203721029MaRDI QIDQ2058645
Zurab K. Silagadze, Shailesh Dhasmana, Abhijit Sen
Publication date: 9 December 2021
Published in: Annals of Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2106.09523
Hamilton's equations (70H05) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Applications of differential geometry to physics (53Z05)
Related Items
Third quantization for scalar and spinor wave functions of the Universe in an extended minisuperspace ⋮ Spinorial Wheeler–DeWitt wave functions inside black hole horizons ⋮ Eisenhart lift of Koopman-von Neumann mechanics ⋮ Hidden symmetry of the static response of black holes: applications to Love numbers ⋮ Dynamics of entropy and information of time-dependent quantum systems: exact results ⋮ Particle motion in circularly polarized vacuum pp waves ⋮ Free to harmonic unitary transformations in quantum and Koopman dynamics*
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Kohn's theorem, Larmor's equivalence principle and the Newton-Hooke group
- Nonrelativistic gauged quantum mechanics: From Kaluza-Klein compactifications to Bargmann structures
- The dramatic episode of Sundman
- The geometry of Schrödinger symmetry in non-relativistic CFT
- Contact geometry in Lagrangian mechanics
- Eisenhart lifts and symmetries of time-dependent systems
- On useful conformal transformations in general relativity
- Theory of gravitational interactions
- Linearization: geometric, complex, and conditional
- Anharmonic quantum mechanical systems do not feature phase space trajectories
- On generalized Sundman transformation method, first integrals, symmetries and solutions of equations of Painlevé-Gambier type
- Equivalence Principle, Quantum Mechanics, and Atom-Interferometric Tests
- The quantum Arnold transformation
- Equivalence between focused paraxial beams and the quantum harmonic oscillator
- Schrödinger manifolds
- Classical aspects of lightlike dimensional reduction
- Projective geometry of systems of second-order differential equations
- Dynamics of meromorphic maps : maps with polynomial schwarzian derivative
- From Triangles to Manifolds
- Symplectic geometry
- The Cotton tensor in Riemannian spacetimes
- Penrose limits and spacetime singularities
- Embedding Galilean and Carrollian geometries. I. Gravitational waves
- Niederer’s transformation, time-dependent oscillators and polarized gravitational waves
- First Steps in Differential Geometry
- A Remarkable Property of Plane Waves in General Relativity
- A brief history of contact geometry and topology.
This page was built for publication: Equivalence of a harmonic oscillator to a free particle and Eisenhart lift
