structural:scholar_edition, linguistic:voice_change
Derivation

On the other hand, in the interval x ∈ {\displaystyle x\in } we have V avg ε ′ = ∫ − ε ε d x V (x) | ψ ′ | 2 = ε 2 | c | 2 1 + 4 3 | c | 2 ε 3 ∫ − ε ε d x V (x) ≃ 2 ε 3 | c | 2 V (0) + ⋯, {\displaystyle {V_{\text{avg}}^{\varepsilon }}'=\int _{-\varepsilon }^{\varepsilon }dx\,V(x)|\psi '|^{2}={\frac {\varepsilon ^{2}|c|^{2}}{1+{\frac {4}{3}}|c|^{2}\varepsilon ^{3}}}\int _{-\varepsilon }^{\varepsilon }dx\,V(x)\simeq 2\varepsilon ^{3}|c|^{2}V(0)+\cdots,} which holds to order ε 3 {\displaystyle \varepsilon ^{3}}.