Solutions of the Schrödinger equation for the time-dependent linear potential
| dc.creator | Shen, Jian Qi | |
| dc.date | 2003-10-30 | |
| dc.date.accessioned | 2026-07-07T06:08:12Z | |
| dc.date.available | 2026-07-07T06:08:12Z | |
| dc.description | By making use of the Lewis-Riesenfeld invariant theory, the solution of the Schrödinger equation for the time-dependent linear potential corresponding to the quadratic-form Lewis-Riesenfeld invariant $I_{\rm q}(t)$ is obtained in the present paper. It is emphasized that in order to obtain the general solutions of the time-dependent Schrödinger equation, one should first find the complete set of Lewis-Riesenfeld invariants. For the present quantum system with a time-dependent linear potential, the linear $I_{\rm l}(t)$ and quadratic $I_{\rm q}(t)$ (where the latter $I_{\rm q}(t)$ cannot be written as the squared of the former $I_{\rm l}(t)$, {\it i.e.}, the relation $I_{\rm q}(t)= cI_{\rm l}^{2}(t)$ does not hold true always) will form a complete set of Lewis-Riesenfeld invariants. It is also shown that the solution obtained by Bekkar {\it et al.} more recently is the one corresponding to the linear $I_{\rm l}(t)$, one of the invariants that form the complete set. In addition, we discuss some related topics regarding the comment [Phys. Rev. A {\bf 68}, 016101 (2003)] of Bekkar {\it et al.} on Guedes's work [Phys. Rev. A {\bf 63}, 034102 (2001)] and Guedes's corresponding reply [Phys. Rev. A {\bf 68}, 016102 (2003)]. | |
| dc.description | six pages; Latex; I think that this paper will be a supplement to the recent comment [Phys. Rev. A {\bf 68}, 016101 (2003)] of Bekkar {\it et al.} on Guedes's work [Phys. Rev. A {\bf 63}, 034102 (2001)] and Guedes's reply to Bekkar {\it et al.}'s comment | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0310179 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0310179 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/91545 | |
| dc.subject | Quantum Physics | |
| dc.title | Solutions of the Schrödinger equation for the time-dependent linear potential | |
| dc.type | text |