J2 J2 J2 JJJ
J2 J2 J2 JJJ
Here, IA, , and IC are the moments of inertia about the principal axes of rotation, while JA, Jb , and JC are the corresponding projections of the total angular momentum vector J. The
Figure 5.10 Molecular structure of NH3, showing the three principal axes of rotation.
principal axes for NH3 are also shown in Figure 5.10. The molecule is a symmetric top, where two of the axes, here labeled B and C, have identical moments of inertia. Note that IA < IB, i. e., the molecule is a prolate (as opposed to oblate) rotator. In the absence of external torques, a symmetric top rotates about its symmetry (A) axis, which in turn precesses about the fixed vector J (Figure 5.11). The scalars J and JA are therefore both constants of the motion.
To find the quantum mechanical energy levels, we first use the equality of IB and IC to rewrite equation (5.17) as
Since J and JA are conserved classically, the generalization of equation (5.6) is
Axis A
Axis A
Figure 5.10 Molecular structure of NH3, showing the three principal axes of rotation.
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