This preview shows page 1. Sign up to view the full content.
Unformatted text preview: system: particle on a ring/particle on a sphere by Schrodingers approach and Diracs algebra. Later, we will apply it to understand/predict rotational spectroscopy.) The time-independent Schrodinger equation (in the spherical coordinate system) for the rotational motion of a diatomic molecule such as I 2 is shown in Engel Eq. (7.17). This is also the TISE for a particle on a sphere. (a) Please prove by algebra that the spherical harmonics function Y 1,+1 (i.e., l quantum number =1, m quantum number =+1) is indeed a solution to Eq. (7.17). (b) What is the corresponding eigenvalue E? [Hint: Plug the functional form of Y 1,+1 into Eq. (7.17) and show LHS=RHS. You can find the functional form of Y 1,+1 on p. 116 of Engels and the correct answers for E in Eq. (7.26)]...
View Full Document
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
- Quantum Chemistry