{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

This preview shows pages 1–8. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Classical Hamiltonian of effective particle Quanum Mechanical formulation: Find eigenfunctions and eigenvalues of the Hamitonian:
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Note: also classically rotations about different axis do not commute
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

{[ snackBarMessage ]}

### Page1 / 8

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

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online