On the four Euclidean conformal group structure of the Sturmian operator

The Sturmian method consists in replacing the eigenvalue problem for the interacting particle Hamiltonian (Schroedinger equation) by the spectral problem for the so-called Sturmian operator (coupling constant quantization). The latter is almost always compact. The main result of this work lies in the disclosure of the algebraic nature of the Sturmian operator as a 'linear superposition' of group representation operators. This group theoretical understanding leads to a large field of physical applications. (Auth.)