= Ramp-state expansion in a symmetric infinite well
{title2=$c_n=-2\sqrt3(-1)^n/(n\pi)-4\sqrt3\sin(n\pi/2)/(n^2\pi^2)$}
In a well $-a<x<a$, the normalized state proportional to $x$ on $0<x<a$ and zero elsewhere has stationary-state coefficients
$$
c_n=-\frac{2\sqrt3(-1)^n}{n\pi}-\frac{4\sqrt3\sin(n\pi/2)}{n^2\pi^2}.
$$
They follow from the <orthonormal basis> inner products. Their squared magnitudes give energy-measurement probabilities by the <Born rule>; splitting even and odd indices in the <Parseval identity> gives convergent integer-coefficient series identities. The expansion is interpreted in the square-integrable state norm.
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