Finite Element Approach to the Vibrational Schrödinger Equation of Diatomic Species

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Abstract
The finite element approach was successfully applied to the vibrational Schrödinger equation of diatomic species. An O2 molecule with a harmonic potential and an Ar2 molecule with a Lennard-Jones potential were examined and their eigen values and the associated eigen function were obtained. The calculated eigen values of the O2 molecule agree with those expected. In the case of the Ar2 molecule the calculated eigen values agree with those experimentally obtained when Lennard-Jones parameters are ε=115.1 (cm−1) and σ=3.35 (Å). This verifies the validity of the present approach.