The Study Of Analytic Wave Function For Ground State Of H₂⁺

The interaction of strong laser field and molecule will produce a lot of interesting phenomenon, such as high harmonic generation and above threshold ionization. In order to figure out physics from these phenomenon, theoretical physists needs the analytical wave function of the molecule. H₂⁺, as the simple molecule, become the object under study. But even for H₂⁺, there was no exactly accurate analytic function. So people have to use the approximate analytic function . As for H₂⁺, people often used the linear combination of atomic function to represent H₂⁺ wave function for ground state, that was(?), where z represented the effective positivecharge seen by the electron. This dissertation focused on the accuracy of thisfunction by studying its influence on potential energy vibrational levels of the ground state of H₂⁺.(1) We obtained the potential energy analytic expression for ground state of H₂⁺ as a function of z by using Hamitonian of H₂⁺ and that approximate wave function. While calculation the integral, we used the elliptical coordinates.(2)RKR potential was calculated based on the experimental spectral data. By comparing with RKR potential, we found when z=1.23 , the analytic expression agree with RKR potential at experimental equilibrium position. But when internuclear separation increases, it begins to deviate the RKR potential.(3)We calculated the vibratinal energy levels of ground state of H₂⁺ by substitute the potential expression into the Schrodinger equation for nuclear. And we compared them with experimental vibrational energy levels, we found that when z=1.13, the vibrational energy levels agree with each other most.