The Spherical Top

Examples: CH4, CCl4, SF6

The rotational energy is given for I = IA = IB = IC :

E = JA² + JB² + JC²/2I = J²/2I

We obtain the corresponding quantum-mechanical equation whether we change to operators H and J:

Hy = J²/2I y = E y

The eigenvalues of J² are as follows: J² y = J(J + 1)h²y

where J = 0, 1, 2, ...

→ EJ = h²/2I J (J + 1)

The first factor can be shortened into the rotational constant B [in wavenumbers]:

EJ = B · J (J + 1) where J = 0, 1, 2, ... B, EJ [cm-1]

B [cm-1] = h/4πc I B [J] = B [cm-1] · hc

c is the speed of light