Ladder operators of group matrix elements

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Abstract
All ladder operators and some recurrence relations of the matrix elements of certain group elements of SO(3), SO(2,1), E(2), SO(4), SO(3,1), and E(3) have been explicitly determined and the underlying factorizations of the second‐ and the fourth‐order linear ordinary differential equations in terms of first‐ and second‐order ladder operators have been transparently demonstrated as an extension to the Schrödinger–Infeld–Miller factorization. These ladder operators are very useful in physical applications where the corresponding matrix elements represent certain physical transitions.