Spectrum of potentials gr-(s+2) via SL(2,R) acting on quaternions

Potentials of the r-(s+2) power type are studied as the superposition of Yukawa potentials. The SL(s,R) group acting on the quadrivector impulsion considered as a quaternion generates a compact self-adjoint operator deduced from the Schrodinger operator by a Fourier-Fock transformation. The operator is approximated by finite rank operators and gives the spectrum of energy as a function of the coupling constant, the angular momentum and the exponent s.