A new realisation of dynamical groups and factorisation method

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Abstract
A new method of algebraisation of quantum mechanical eigenvalue equations is presented. In this method the dynamical algebra is represented on the space of group matrix elements. The ladder operators of the dynamical algebra are obtained from Infeld-Hull-Miller factorisations. The method is used to study the first Poschl-Teller equation even in the non-symmetric case. The energy spectrum and the exact normalised solutions are obtained in agreement with the results of non-algebraic methods.