Rotational kinetic energy operator

The rotational kinetic energy operator for a rigid polyatomic molecule is shown in Appendix G to be... 

The simplest example of the way in which the various terms arise in the effective electronic Hamiltonian involves the rotational kinetic energy operator, 3Qot ... 

Thus we see that the operator g is not strictly an angular momentum operator in the quantum mechanical sense, which is why we have assigned it a different symbol. More importantly for the present purposes, we cannot use the armoury of angular momentum theory and spherical tensor methods to construct representations of the molecular Hamiltonian. In addition, the rotational kinetic energy operator, equation (7.89), takes a more complicated form than it has for a nonlinear molecule where there are three Euler angles (rotational coordinates). 

In the isomorphic Hamiltonian, the rotational kinetic energy operator has the simpler (and familiar) form... 

N. C. Handy, The derivation of vibration-rotation kinetic energy operators, in internal... 

J. Pesonen, Vibration-rotation kinetic energy operators A geometric algebra approach. J. Chem. Phys. 114, 10598-10607 (2001). 

The operator between the brackets is the harmonic oscillator Hamiltonian, which has the basis functions (112) as its eigenfunctions the remaining term is taken into account via Eq. (114). The rotational kinetic energy operator L(cuP) [Eq. (26)] can be written in terms of the shift operators J = J, + iJi, and the operator J, which act on the basis as... 

The advances of the next few years after the appearance of Molecular collisions. VIII are summarized in a chapter in a book edited by Bernstein (also at Wisconsin and a collaborator with Curtiss) [23]. The next major impetus to this approach to molecular collisions came in the period 1973-74 with the publication of two papers [18, 19] dealing especially with the CS approximation. One paper is by a former student of Hirschfelder and the other involves one of the present authors. The relationship between these two papers can best be seen by a brief consideration of how each treated the orbital rotational kinetic energy operator. Both papers used rotating-frame ideas and the Hamiltonian written either in the form... 

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