Abstract
Lie's method of extended-group theory has been used to obtain explicit forms of the generators and the structure constants of the maximal symmetry group of point transformations for the nonrelativistic Schr\"odinger equation. For atoms and molecules this symmetry group is an infinite-parameter Lie group with an infinite-parameter invariant subgroup. The corresponding factor group is a 14-parameter Lie group containing a proper subgroup locally isomorphic to SO(4), the orthogonal group in four dimensions.
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