Zero-order wave function degeneracy

The first-order corrections to energy and the zero-order wave functions, with expansion coefficients c, are obtained as the eigenvalues and eigenfunctions. Because the matrix V generally has p different eigenvalues, the degeneracy of the refer-... 

We must modify perturbation theory to apply it to an energy level that is degenerate in zero order. For example, the two configurations (ls )(2s) and ( s)(2p) of the helium atom correspond to several states that have the same energy in zero order. We assume the same kind of Hamiltonian as in Eq. (G-1) and consider a zero-order energy level with a degeneracy equal to g. We have g zero-order wave functions. We call them the initial zero-order functions. Unfortunately, there is no guarantee that each of these functions would turn smoothly into one of the exact wave functions if A. is increased from 0 to 1. 

If the solution of the zero-order Schiodinger equation [i.e., all teiins in (17) except V(r,Ro) are neglected] yields an/-fold degenerate electronic term, the degeneracy may be removed by the vibronic coupling tenns. If F) and T ) are the two degenerate wave functions, then the vibronic coupling constant... 

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