The Spherical Top


Examples: CH4, CCl4, SF6

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

E  =  JA² + JB² + JC²/2I  =  /2I

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

H = /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