Example of quantum systems reduction
| dc.creator | Manjavidze, J. | |
| dc.date | 1998-02-13 | |
| dc.date.accessioned | 2026-07-07T04:24:16Z | |
| dc.date.available | 2026-07-07T04:24:16Z | |
| dc.description | To solve the quantum-mechanical problem the procedure of mapping onto linear space $W$ of generators of the (sub)group violated by given classical trajectory is formulated. The formalism is illustrated by the plane H-atom model. The problem is solved noting conservation of the Runge-Lentz vector $n$ and reducing the 4-dimensional incident phase space $T$ to the 3-dimensional linear subspace $W=T^* V\times R^1$, where $T^* V$ is the (angular momentum ($l$) - angle ($\vp$)) phase space and $R^1 =n$. It is shown explicitly that (i) the motion in $R^1$ is pure classical as the consequence of the reduction, (ii) motion in the $\vp$ direction is classical since the Kepler orbits are closed independently from initial conditions and (iii) motion in the $l$ direction is classical since all corresponding quantum corrections are defined on the bifurcation line ($l=\infty$) of the problem. In our terms the H-atom problem is exactly quasiclassical and is completely integrable by this reasons. | |
| dc.description | 9 pp, Latex, no figure | |
| dc.identifier | https://arxiv.org/abs/hep-th/9802098 | |
| dc.identifier | http://arxiv.org/abs/hep-th/9802098 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/55343 | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Example of quantum systems reduction | |
| dc.type | text |