Algebraic approach to matrix elements: Recurrence relations and closed formulas for hydrogenlike wave functions

An algebraic approach to obtain ladder operators for hydrogenlike wave functions from the algebraic representation of the Lₙᵏ Laguerre associated polynomials directly involved is presented. The method leads to diverse ladder operators depending on the manner as the operational form of Lₙᵏ is used. As an example, this work deals with linear creation and annihilation operators of two kinds: some that influence the n energy quantum number and others acting on the l orbital number according to usual ladder properties. In addition, as a useful application of the raising and lowering operators thus obtained, generalized recurrence relations and closed formulas for the calculation of multipole matrix elements are algebraically deduced by means of a procedure that takes advantage of the relationship between the ladder operators associated with the bra and those related to the ket.