L13 - L 2 and substitute into the expression of the...

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Rigid rotations Classical Hamiltonian L = angular momentum; L = I w I = moment of Inertia; I = m r 2 w = angular velocity Kinetic energy Model for a rotating diatomic molecule
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Classical Hamiltonian of effective particle Quanum Mechanical formulation: Find eigenfunctions and eigenvalues of the Hamitonian:
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In Q.M.: Angular momentum components do not commute! A system cannot have well defned angular momentum around the x, y, and z axes L 2 and L x (L y and L z ) do commute
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Note: also classically rotations about different axis do not commute
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Quanum Mechanical formulation: Find eigenfunctions and eigenvalues of the Hamitonian: Use polar coordinates to express the Hamiltonian Express component of angular momentum in polar coordinates; compute
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Unformatted text preview: L 2 and substitute into the expression of the Hamiltonian Angular Momenta in polar coordinates Schroedinger Equation for a Rigid Rotor Schroedinger Equation for a Rigid Rotor Eigenvalues Spacing between Eigenvalues is NOT constant: it increases with angular momentum J Absorption frequencies of the order of ~ 2-10 10 to 10 11 Hz in diatomic molecules microwave region n Spacing between Eigenvalues is NOT constant: it increases with angular momentum J Absorption frequencies of the order of ~ 2-10 10 to 10 11 Hz in diatomic molecules microwave region n n = 2B ( J+1) with B = rotational constant...
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This note was uploaded on 02/06/2011 for the course CHE 110A taught by Professor Mccurdy during the Fall '09 term at UC Davis.

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L13 - L 2 and substitute into the expression of the...

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