Partial wave analysis

Partial wave analysis, in the context of quantum mechanics, refers to a technique for solving scattering problems by decomposing each wave into its constituent angular momentum components and solving using boundary conditions.

The following description follows the canonical way of introducing elementary scattering theory. A steady beam of particles scatters off a spherically symmetric potential ${\displaystyle V(r)}$, which is short ranged so that for large distances ${\displaystyle r\to \infty }$, the particles behave like free particles. In principle, any particle should be described by a wave packet but we describe the scattering of a plane wave traveling along the z-axis ${\displaystyle \exp(ikz)}$ instead, because wave packets are expanded in terms of plane waves and this is mathematically simpler. Because the beam is switched on for times long compared to the time of interaction of the particles with the scattering potential, a steady state is assumed. This means that the stationary Schrödinger equation for the wave function ${\displaystyle \Psi (\mathbf {r} )}$ representing the particle beam should be solved:

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