Global Symmetries of Time-dependent Schrödinger Equations
نویسنده
چکیده
Some symmetries of time-dependent Schrödinger 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) j s T2(R) of the SL(2, R) with a two-dimensional real translation group T2(R). Here, the time variable t transforms as t → t = (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.
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