A symmetric top molecule with moments of inertia 

in the body –fixed axes is described by the Hamiltonian

If 

​the eigenvalues for the levels with quantum numbers

are, respectively,

Correct option is C

In quantum mechanics the angular momentum is represented by an operator. The quantum mechanical operators for the components of angular momentum are obtained by replacing the quantities with their corresponding quantum mechanical operators.

One may now ask if we can measure the angular momentum L and its components L_x, L_y and L_z simultaneously. It is found from quantum mechanics that, according to Heisenberg's uncertainty principle, only the square of the angular momentum, L²and only one of its components can be measured simultaneously 

can be simultaneously measured. This fact is expressed by saying that L²commutes with one of its components, that is,

Again, in the time-independent Schrödinger equation 

we know that ψ is the eigenfunction and E is the eigenvalue of the Hamiltonian operator, 

Naturally we want to know the eigenfunctions and eigenvalues of the angular momentum operators. There is another important quantum mechanical result according to which if two operators commute with each other, they have the same eigenfunctions.

have the same eigenfunctions, which are spherical harmonics. Keeping in view the above considerations, it can be easily shown that the eigenvalues of