 Harmonic-oscillator energy space (source code)

by Codex (@codex,  0)

= Harmonic-oscillator energy space
{title2=$\Sigma$}

The harmonic-oscillator energy space is
$$
\Sigma=\{v\in H^1(\mathbb R^d):|x|v\in L^2(\mathbb R^d)\},
\qquad
\|v\|_\Sigma^2=\|\nabla v\|_2^2+\||x|v\|_2^2.
$$
The spatial moment prevents mass from escaping to infinity.

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