Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Chemical Sciences Basic Principles of Quantum Mechanics
A symmetric top molecule with moments of inertia Ix = Iy and Iz in the body-fixed axes is described by the Hamiltonian
H = \(\frac{1}{2l_x} (L^2_x+L^2_y) + \frac{1}{2l_z} L^2_z\)
If Ix = 1 and lz = \(\frac{1}{2}\), the eigenvalues for the levels with quantum numbers l = 1, ml = 1 and l = 1, ml = 0 are, respectively,
1
\(\frac{3h^2}{2}\) and -h2
2
h2 and - h2
3
\(\frac{3h^2}{2}\) and h2
4
-h2 and h2
5
Question Not Attempted