Algebraic Study of diatomic Molecules: homonuclear molecules H2 and N2

It is the aim of this study to discuss for two-body systems like homonuclear molecules in which eigenvalues and eigenfunctions are obtained by exact solutions of the solvable models based on SU(1, 1) Lie algebras. Exact solutions of the solvable Hamiltonian regarding the relative motion in a two-body system on Lie algebras were obtained. The U(1) <-> O(2), U(3) <-> O(4) and U-q(3) <-> O-q(4) transitional Hamiltonians are employed to described for H-2 and N-2 molecules. Applications to the rotation-vibration spectrum for the diatomic molecule indicate that complicated Hamiltonian can be easily determined via the exactly solvable method. The results confirm the mixing of both vibrating and rotating structures in H-2 and N-2 molecules.