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  "body": "\n## Summary\n\nThe Born series is the expansion of a scattered wave in powers of the scattering potential.\nIt is obtained by iterating the [[Lippmann–Schwinger equation|MW5R19P2X4]] $\\psi = \\phi + G_0 V \\psi$, which gives $\\psi = \\phi + G_0 V \\phi + G_0 V G_0 V \\phi + \\cdots$.\nIt is the [[Liouville–Neumann series|H1HWSWME6B]] of this integral equation.\nSo it converges when the operator $G_0 V$ is small, for example for weak potentials or at high energy.\nIts first term beyond $\\phi$ is the Born approximation, the standard first estimate of scattering amplitudes.\n\n## Explanations\n\n### L1 human\n\nA wave meets an obstacle and is scattered once, then the scattered wave is scattered again, and so on.\nThe Born series adds up these contributions: no scattering, one scattering event, two events, and so on.\nWhen the obstacle is weak, each extra event is much smaller than the last, so the first one or two terms already give a good answer.\n",
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