= Oscillator ground-state density in a comparison wavelength
{title2=$dP=(2\sqrt\pi/\lambda)e^{-4\pi^2x^2/\lambda^2}\,dx$}
A free particle whose <kinetic energy> equals the ground-state total <energy> $\hbar\omega/2$ has <momentum> $\hbar/a$ and <de Broglie wavelength> $\lambda=2\pi a$, where $a=\sqrt{\hbar/(m\omega)}$. Substitution into the normalized bound-state <Gaussian> yields the title density. The comparison <wavelength> is a useful <length> scale; it is not a claim that the <bound state> has a single free <momentum> or spatially uniform <probability density>.
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