Abstract: The vibrational model of linear polyatomic molecule is adopted, choosing atomic displacements along and perpendicular to bond axis as the internal coordinates, multidimensional coupling oscillators and outstripping quadratic power terms of the potential function, respectively, as zero order approximation and perturbation. The vibration of linear polyatomic molecule are generally solved utilizing general linear quantum transfor- mation theory and stationary state perturbation theory. Finding the solution of the oscillator＇ s eigenvalue and state for linear polyatomic molecule is changed into the diagonalization of semi-positive and positive definite matrices. Perturbation matrix elements, all of the different levels energy and perturbation corrects of wave function are calculated in the representation of multidimensional non-coupling oscillators. And as a example CO2 molecule is particularly solved.

Key words: linear polyatomic molecule, linear quantum transformation, stationary state perturbation theory, perturbation correct