A new study on Λ splitting of electronic states of linear molecules
线型分子的电子能级之Λ分裂的新解释

The electronic states of a linear molecule are the eigen-vectors of the projectional component of electron's angular momentum operator along the direction of the molecular axis, because the molecular axis is a symmetric axis of the Hamiltonian of the linear molecule. If an electronic energy eigen-state has a non-zero eigen-value of the angular momentum, the state would be a double-degenerated state, which is composed of two states that have respectively reverse eigen-values of the angular momentum. Due to something of coupling effect in the molecule, the degenerated doublet of the electronic state splits into two states, which have different eigen-values of energy and reverse eigen-values of the angular momentum. The coupling of electron angular momentum and molecule rotation momentum plays the most important role in the splitting of the doublet of the electronic state. But the coupling of these two kinds of angular momentum, in essence, is a result of the entanglement between the movement of electrons and molecular frame, not real coupling interaction of the two angular momenta. In this paper, classic dynamics is first used to study the rotation of a linear molecule as a rigid rotor with a fixed attached angular momentum and Euler's and Lagrange's equations for the rotation of the linear molecule has been deduced. After constructing an extensive potential function to express the inertial moment created by the fixed attached angular momentum, Hamiton function and the corresponding Hamilton equations of the rotation of the linear molecule are both achieved. The Hamilton function has been foune to be regular quadratic, and therefore the correlative Hamiltonian for the rotation of the linear molecule is also obtained by complying with Bohr's correspondence principle and the construction rules of operator in quantum theory. The Hamiltonian has also been re-written into two parts as J.H.Van.Vleck has done and the resultant expressions are exactly the same as J.H.Van.Vleck's famous result. But the deduction in the paper is much more explicit than that of J.H.Van.Vleck.