Quantum Chemistry 6.12 – Angular Momentum Eigenvalues

Short lecture on the eigenvalues of rigid rotor wavefunctions.

The Hamiltonian operator of the rigid rotor quantum mechanical model system can be expressed in terms of the total angular momentum squared operator. Thus, the rigid rotor wavefunctions (spherical harmonics) are eigenfunctions of the total angular momentum squared operator, with an eigenvalue of [ hbar^2 J(J+1) ]. Additionally, these wavefunctions are eigenfunctions of the z-component angular momentum operator Lz, with an eigenvalue of [ hbar m ]. These wavefunctions are not eigenfunctions of Lx or Ly.

Notes Slide: http://i.imgur.com/lVMqzKR.png

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