(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I'm just having trouble seeing how to determine whether or not a wave of definite angular momentum will couple to a given term. The context is in G.P. Lepage'sHow To Renormalize The Schrodinger Equation,in which he derives the following renormalized potential

[tex] V_{eff}(\mathbf{r}) = -\frac{\alpha}{r}erf(r/\sqrt{2}a) + ca^2\delta^3_a(\mathbf{r}) + d_1a^4\nabla^2\delta^3_a(\mathbf{r}) + d_2a^4\nabla \cdot \delta^3_a(\mathbf{r})\nabla. [/tex]

The details aren't too important, but he parenthetically states at a later time that "it is obvious that the [itex] d_2 [/itex] term couples only two P-waves in the limit [itex] a \rightarrow 0 [/itex]. When [itex] a [/itex] is nonzero, however, this term has a small residual coupling to S-waves." I'm not sure how he's seeing any of this. I know that P-waves have angular momentum eigenvalue l = 1, but what does this imply about what's coupled to what?

2. Relevant equations

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3. The attempt at a solution

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# S-Wave vs P-Wave Coupling

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