A general method for constructing first-order symmetry operators for the stationary Schrödinger and Pauli equations is proposed. It is proven that the Lie algebra of these symmetry operators is a one-dimensional extension of some subalgebra of an e(3) algebra. We also assemble a classification of stationary electromagnetic fields for which the Schrödinger (or Pauli) equation admits a Lie algebra of first-order symmetry operators.
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 132–139, October, 2016.
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Boldyreva, M.N., Magazev, A.A. On the Lie Symmetry Algebras of the Stationary Schrödinger and Pauli Equations. Russ Phys J 59, 1671–1680 (2017). https://doi.org/10.1007/s11182-017-0959-0
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DOI: https://doi.org/10.1007/s11182-017-0959-0