Two and three dimensional Hamiltonians with generalized and ordinary shape invariance symmetry

Panahi H., Jafarizadeh M.A.

Two and three dimensional Hamiltonians with generalized and ordinary shape invariancesymmetry have been obtained by Fourier transforming over some coordinatesof the SU(3) Casimir operator defined on SUs3d/SUs2d symmetric space. It isshown that the generalized shape invariance of the two dimensional Hamiltonian isequivalent to SU(3) symmetry while in the three dimensional one, the ordinaryshape invariance is equivalent to contracted SU(3) and there is one to one correspondencebetween the representations of the generalized shape invariance symmetryof the two (three) dimensional Hamiltonian and SU(3) [contracted SU(3)]Verma bases.