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Solutions of the Schrödinger equation for the time-dependent linear potential | | Jian Qi Shen
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30 Oct 2003 | | Subject: | quant-ph | | Abstract: | 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 $I_{
m q}(t)$ 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 $I_{
m l}(t)$ and quadratic $I_{
m q}(t)$ (where the latter $I_{
m q}(t)$ cannot be written as the squared of the former $I_{
m l}(t)$, {it i.e.}, the relation $I_{
m q}(t)= cI_{
m l}^{2}(t)$ 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 $I_{
m l}(t)$, one of the invariants that form the complete set. In addition, we discuss some related topics regarding the comment [Phys. Rev. A {f 68}, 016101 (2003)] of Bekkar {it et al.} on Guedes’s work [Phys. Rev. A {f 63}, 034102 (2001)] and Guedes’s corresponding reply [Phys. Rev. A {f 68}, 016102 (2003)]. | | Source: | arXiv, quant-ph/0310179 | | Services: | Forum | Review | PDF | Favorites | |
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