2003/06/26 by Karmadeva Maharana, Maharana, Karmadeva
Engineering · Mathematics · Physics and Astronomy · #Crystallography and Radiation Phenomena #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Particle Accelerators and Free-Electron Lasers #Quantum and Classical Electrodynamics #hep-th #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.math-ph/0306069
12 pages
arxiv created 2003/06/26 · openalex publication_date 2003/06/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We analyze the classical equations of motion for a particle moving in the presence of a static magnetic field applied in the z direction, which varies as 1\overx2 . We find the symmetries through Lie's method of group analysis. In the corresponding quantum mechanical case, the method of spectrum generating su(1,1) algebra is used to find the energy levels for the Schroedinger equation without explicitly solving the equation. The Lie point symmetries are enumerated. We also find that for specific eigenvalues the vector field contains 1\overx \p\over\p x and 1\over x2 \p\over\p x type of terms and a finite Lie product of the generators do not close.