QS 20: Partial Wave Expansion

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$\newcommand{\kk}[1]{|#1\rangle}
\newcommand{\bb}[1]{\langle #1}
\newcommand{\vv}[1]{{\bf #1}}$


For a central potential $V=V(r)$, both $H$ and $H_0$ commute with rotations. Therefore the Moller operators, S- and T-matrices all commute with rotations as well. In such a case the useful basis is $\kk{E,l,m}$ which are the free particle energy angular momentum eigenstates. Its inner product with momentum eigenstates (which are also energy eigenstates) is
\begin{eqnarray*} \bb{\vv{k}}\kk{E,l,m} = \end{eqnarray*}

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