Symplectic sp(4) spectrum generating algebra for a large class of quantum three-body problems

We demonstrate that a realization of the sp(4) symplectic algebra can be used as a spectrum generating algebra for a large class of hamiltonian operators written in two coordinates, r1 and r2, and their conjugate momenta. The physical operators are mapped to step and weight operators of sp(4) and these are mapped to 4-modes boson operators that allow a straightforward exact calculation of matrix elements. Several important three-body quantum hamiltonian can be written using the algebra elements as building blocks. Some cases and applications are discussed.