Unformatted text preview: L 2 operator is defined as: L 2 = L x 2 + L y 2 + L z 2 . Please use Eq. (7.31) and commutator formula (ref. lecture notes or formula sheets) to prove that L 2 and L z commute, i.e., [ L 2 , L z ] = 0. [1](b) According to the “common eigenket theorem”, therefore L 2 and L z can share common eigenfunctions, which are spherical harmonics Y l,m . Please use the l =1 m =+1 spherical harmonics Y 1,+1 as an example to prove by algebra that it is indeed an eigenfunction L z . Please calculate the corresponding eigenvalue. [Hint: you can find L z in Eq. (7.30)]...
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This note was uploaded on 03/29/2009 for the course CHEM 113A taught by Professor Lin during the Winter '07 term at UCLA.
 Winter '07
 Lin
 Quantum Chemistry

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