Hi, I'm reading about the partial wave expansion in Shankar. In his method, we expand the incident plane wave (he chooses it such that it's coming in along the z axis, and using spherical coordinates) using the Legendre polynomials:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]e^{ikr cos(\theta)} = \sum _{l = 0} ^\infty i^l (2l + 1) j_l(kr)P_l(cos(\theta))[/tex]

Then he says that "since the potential conserves angular momentum, each angular momentum component scatters independently". I get what he's saying, but my question is: Why couldn't the values of j_l(kr) switch around such that the various angular momentum components switch around, but the total amount is still conserved?

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Scattering partial wave expansion question

**Physics Forums | Science Articles, Homework Help, Discussion**