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?

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# Scattering partial wave expansion question

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