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  "body": "\n## Summary\n\nThe spherical Bessel functions $j_n$ and $y_n$ are the Bessel functions of half-integer order $n + \\frac{1}{2}$, rescaled by $\\sqrt{\\pi / (2x)}$.\nThey solve the radial part of the Helmholtz equation in spherical coordinates.\nThey are elementary: each is a combination of $\\sin x$, $\\cos x$ and powers of $x$.\nThey describe waves scattered by a sphere and the radial motion of a free quantum particle.\n\n## Explanations\n\n### L1 human\n\nWhen a wave spreads out from a point in space, its strength along each ray is described by a spherical Bessel function.\nThe simplest one is $j_0(x) = \\frac{\\sin x}{x}$, a sine wave whose size falls off like $\\frac{1}{x}$.\nThe next one is $j_1(x) = \\frac{\\sin x}{x^2} - \\frac{\\cos x}{x}$.\nHigher ones come from a simple recurrence, so they can all be written with sines, cosines and powers.\n",
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