68110863-5-Problems

68110863-5-Problems - operator 7 What is the eigenvalues of...

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Problems on Angular momentum 1. Find Earth angular momentum using Earth-Sun distance and mass of Earth? (Earth - Sun distance m, Mass of the Earth kg) Solution For an orbit, angular momentum is conserved, and this leads to one of Kepler's laws. For a circular orbit, angular momentum is The average angular momentum is , treating the Earth as if it were a point mass. Mean distance from Earth to Sun is km (8.31 minutes at the speed of light) Mass of the Earth is kg. Earth takes 365 days to go one complete circle around Sun. Average angular momentum . 2. Verify the following commutation relations Using the explicit relations 3. Is orbital angular momentum of the electron conserved, in the hydrogen atom? 4. Is orbital angular momentum of the electron quantized, in the hydrogen atom? 5. Where does the physical meaning of centrifugal potential barrier come, in the radial part of the Schrödinger equation? 6. Determine eigenvalues and normalized eigenfunction of the angular momentum

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Unformatted text preview: operator . 7. What is the eigenvalues of the . 8. Rotational energy spectrum of a molecule arises from the Hamiltonian Where are moments of inertia along the axes . If the moments of inertias calculate rotational energy of the molecule? For a rigid rotator Calculate rotational energy of rotator. 9. Eigenvalue equation of the is given by For which values of the the following functions solutions of equation: 10. Using the definition , show that Satisfy the uncertainty principle. 11. Determine the magnetic moment produced by an electric charge moving along a circular orbit. 12. Show that magnetic moment is proportional to the angular momentum. 13. Write down the spin magnetic moment produced by a charged particle rotating about its axis. 14. Show that the spin matrices Satisfy the commutation relations: 15. Using the definition , show that Satisfy the uncertainty principle....
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This note was uploaded on 01/12/2012 for the course CHEM 133 taught by Professor Staff during the Spring '08 term at UCSD.

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68110863-5-Problems - operator 7 What is the eigenvalues of...

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