Symmetry algebra of the time-dependent Schrödinger equation in constant and uniform fields

The problems of constructing the symmetry operators of the time-dependent Schrödinger equation in the constant and uniform electric and magnetic fields with the use of the obtained operators in the method of non-commutative integration of linear differential equations are considered. A system of defining equations for the first-order symmetry operators is written. The paper investigates the structure of the symmetry algebras. It is shown that in the case of electric field the resulting algebra is the deformation of the Schrödinger algebra sch(1, 3). (paper)