Homework Help Overview
The discussion revolves around calculating the average value of cos(x)^2 over the solid angle of a sphere, specifically addressing why this average equals 1/3. The original poster references a context involving Einstein A and B coefficients and mentions differing approaches from other courses regarding unpolarized, isotropic radiation.
Discussion Character
- Exploratory, Assumption checking, Mathematical reasoning
Approaches and Questions Raised
- The original poster attempts to use an average integral equation but consistently arrives at 1/2 instead of the expected 1/3. They explore integrating from 0 to 2π and using trigonometric identities.
- Some participants suggest that the original poster is not correctly weighting points on the sphere, emphasizing the importance of the uniform probability measure involving sin(x) in the integral.
- Another participant introduces the concept of solid angle and spherical coordinates, proposing a specific integral setup for calculating the average.
Discussion Status
The discussion is ongoing, with participants providing insights into the correct approach for integrating over the solid angle. There are multiple interpretations being explored regarding the weighting of points and the setup of the integral, but no explicit consensus has been reached yet.
Contextual Notes
Participants are addressing potential misunderstandings related to the integration limits and the correct measure for averaging over a sphere. The original poster's attempts indicate a struggle with the mathematical setup required for the problem.