Abstract
The Schrödinger algebra sch3 is examined as a subalgebra of the algebra k1,4 of conformal transformations of the space R1, 4. Orbits of the associated representations of the Schrödinger group are found in the algebra sch3. It is proven that all nontrivial local differential symmetry operators of second order belong to the enveloping algebra U(sch3) of the algebra sch3, and the space of these operators is defined. All the absolute identities and identities on the solutions of the Schrödinger equation are obtained in the space of second-order operators of the algebra U(sch3).
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 120–123, April, 1991.
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Bagrov, V.G., Samsonov, B.F. & Shapovalov, A.V. Some problems of symmetry of the Schrödinger equations. Soviet Physics Journal 34, 382–385 (1991). https://doi.org/10.1007/BF00898109
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DOI: https://doi.org/10.1007/BF00898109