Dynamical symmetry group of the relativistic Coulomb problem in the quasipotential approach

Abstract

i. The algebraic approach in quantum theory, which is known as the theory of dynamical symmetries, is widely applied to the description of the properties of quantum systems [1,2]. The approach is based on the fact that from the operators relating to the studied physical system one can construct various finite-dimensional Lie algebras whose elements are the Hamiltonian and its symmetry operators and also lowering and raising operators, which do not commute with the Hamiltonian. Any Lie algebra determined in this manner is called a dynamical algebra. Independent eigenfunctions of the Hamiltonian form a basis of an irreducible representation of it. Knowledge of the dynamical group (or the algebra) permits complete solution of the quantum-mechanical problem, in particular, determination of the energy levels and wave functions.