 Harmonic-oscillator energy space

ID: harmonic-oscillator-energy-space

Σ = {v \in H^{1} (R^{d}) : ∣ x ∣ v \in L^{2} (R^{d})}, ∥ v ∥_{Σ}^{2} = ∥\nabla v ∥_{2}^{2} + ∥∣ x ∣ v ∥_{2}^{2} .

The spatial moment prevents mass from escaping to infinity.

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