CHEM 35 Lecture Notes - Lecture 4: Horse Length, Wave Function

• School: Stanford University
• Department: Chemistry
• Course: CHEM 35
• Professor: Steven G. Boxer Camille Dreyfus

Document Summary

Since l 2 and l commute, they share common eigenfunctions. These functions are extremely important for the description of angular momentum problems they determine the allowed values of angular momentum and, for systems like the rigid. The first things we would like to know are the eigenvalues associated with these eigenfunctions. We will denote the eigenvalues of l 2 and l z by and , respectively so that: 2 ( , ) = y . ) = y ( , ) For brevity, in what follows we will omit the dependence of the eigenstates on and so that the above equations become. It is convenient to define the raising and lowering operators (note the similarity to the harmonic oscillator! L l il y x. These relations are relatively easy to prove using the commutation relations we"ve already derived: L , l = l , l i l , l .