Question

An H2 molecule (two hydrogen atoms separated by some distance d) may rotate in coordinate space around the origin. The rotation is described by two degrees of freedom, the polar angle and the azimuthal angle p. The Hamilton operator of this system may read 2J where J is the moment of inertia. a) (1P) Determine the cigenvalues, eigenfunctions and possible degrees of degeneracy.

Answer 1

L_z = I_z w_z = I_z d phivariant/dt I = mu R^2 = m_1 m_2/m_1 + m_2 R^2 1/2 Iw^2 = L^2/2L: J = rotational angular momentum H = planckconstantovertwopi^2 partial differential^2/ 2 I partial differential phivariant^2 = L^2 /2I psi H psi = L^2 psi/2I = J(J + 1) planckconstantovertwopi^2 /2I psi (Schrodinger equation) E_J = J(J + 1) planckconstantovertwopi^2/2I (Energy eigen values)

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