Global Symmetries of Time-Dependent Schrodinger Equations
Okubo, Susumu
arXiv, 0303017 / Harvested from arXiv
Text on arXiv
Some symmetries of time-dependent Schr\"odinger equations for inverse quadratic, linear, and quadratic potentials have been systematically examined by using a method suitable to the problem. Especially, the symmetry group for the case of the linear potential turns out to be a semi-direct product $SL(2,R) x T_2(R)$ of the $SL(2,R)$ with a two-dimensional real translation group $T_2(R)$. Here, the time variable $t$ transforms as $t \to t^\prime = (ct+d)/(at+b)$ for real constants $a, b, c$, and $d$ satisfying $bc - ad =1$ with an accompanying transformation for the space coordinate $x$.
Publié le : 2003-03-06
Classification:  Mathematical Physics 
@article{0303017,
     author = {Okubo, Susumu},
     title = {Global Symmetries of Time-Dependent Schrodinger Equations},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0303017}
}

Okubo, Susumu. Global Symmetries of Time-Dependent Schrodinger Equations. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0303017/