Hamiltonian, expansion functions, and coupled equations

The total Hamiltonian including all nuclear degrees of freedom is given in the center-of-mass system by 

For simplicity of the presentation we will hereafter employ the rigid-rotor approximation in which r is fixed at the equilibrium bond distance re of BC.t Note that the potential energy surface (PES) V depends only on the two distances R and r and on the orientation angle 7. 

The wavefunction depends on R and on the four angles Or, pr, 7, and ip. In order to solve the Schrodinger equation, we expand h in terms of parity adapted angular wavefunctions of the form (Launay 1976) 

J = j + 1 is the total angular momentum of the system and M is its projection on the space-fixed 2-axis. Furthermore  

Inserting (11.6) into the time-independent Schrodinger equation and utilizing the orthonormality of the expansion functions leads to the following set of coupled equations for the radial functions Xjn(R JMp)J 

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