Spherical Top

Examples: CH₄, CCl₄, SF₆

For the case of I = I_A = I_B = I_C the rotational energy is given by:

We obtain the respective quantum mechanical equation if we shift to the operators H and J:

The eigenvalues to J² are already known:     J²⋅Ψ =  J(J+1) h²⋅Ψ     with J = 0, 1, 2, ...

It has become common practice to write this equation in a form with the rotational constant B which has the unit of the wavenumber, cm^-1. The product term hcB equals the fraction h²/2I.

With c denoting the speed of light, the transformation between the moment of inertia I and rotational constant B is

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