Spectra of diatomic molecules
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چکیده
Clearly N is perpendicular to R, so the projection of J onto R is the same as the projection LR with eigenvalue ¤1 h of L. (We now reserve z for a direction ̄xed in space, and use the subscript R for a component along R). Because total angular moment of an isolated molecule is constant, eigenfunctions of H when L is non-zero will have the quantum numbers J , MJ , ¤, s (to describe the electronic state), and sn, the sign of ¤. Because L is non-zero, the electronic potential ̄eld in which the nuclei move is no longer really axisymmetric, and N is no longer a good quantum number. However, we may approximate the main e®ect of non-zero L on the nuclear wave functions by replacing the centrifugal term 1 hJ(J + 1)=21R in the nuclear wave equation by one in the expectation value hN2i: " ¡ 1 h 2 21 d dR2 + hN2i 21R2 + Es(R) # F(R) = EF(R):
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