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Symmetries of Equations of Quantum Mechanics
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Reduction of the representations of the generalised Poincare algebra by the Galilei algebra
The realisations of all classes of unitary irreducible representations of the generalised Poincare group P(1,4) have been found in a basis in which the Casimir operators of its important subgroup,Expand
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Conditional symmetry of the equations of nonlinear mathematical physics
We present a survey of results regarding the investigation of the conditions of the symmetry of nonlinear equations of mathematical and theoretical physics: the wave equation, the Schrödinger,Expand
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Separation of variables in two-dimensional wave equations with potential
In the present paper, we solve the problem of separation of variables in the wave equationutt−uxx+V(x)u=0 and give a complete classification of potentialsV(x) forwhich equations of this type admitExpand
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Exact solutions of the d'Alembert and Liouville equations in the pseudo-Euclidean space R2, 2. II
Invariants of the maximal rank-3 and rank-4 subalgebras of the Poincaré algebras AP(2,2), which is the maximal invariance algebra of the d'Alembert equation □u+λuk=0,k=1, and the Liouville equationExpand
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