This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: CHEM 356, Lecture 21, Fall 2009 1 We have previously discussed a procedure whereby the spherical harmonic functions ? , ( , ) could be constructed in terms of , ( , ) and ( ) functions, beginning with a knowledge of the ( ) and , ( ) functions. In many of the standard quan- tum mechanics texts the spherical harmonics are expressed in terms of the ( ) and , ( ) functions, but with the , ( ) functions themselves expressed in terms of associated Legendre polynomials ( ? ) as , ( ) = [ (2 + 1)( )! 2( + )! ] 1 2 ( ? ) . When this format is utilized, the spherical harmonic functions are written as ? , ( , ) = [ (2 + 1)( )! 2( + )! ] 1 2 (cos )e , apart from a phase convention (which we could, as usual, express by multiplying the expression on the righthand side by e ). In this case, there is a standard phase con- vention , introduced by Condon and Shortley in 1935: it is that the spherical harmonics for odd have the sign convention (phase factor) +1 for < 0, 1 for > 0, and that all spherical harmonics having even values of have a phase factor +1. Notice that this phase convention corresponds precisely to what we obtained using ladder operators to construct the more general spherical harmonics from the simpler set of ?...
View Full Document
This note was uploaded on 02/28/2011 for the course CHEM 356 taught by Professor Prof.iaskjd during the Fall '09 term at Waterloo.
- Fall '09