2003/10/30 by Jian Qi Shen, Shen, Jian Qi
Physics and Astronomy · #FOS: Physical sciences #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0310179
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
arxiv created 2003/10/30 · arxiv updated 2009/12/01
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 l2(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)].