structural:summarization, structural:expansion
Derivation

Note that the kinetic-energy densities hold ℏ 2 2 m | d ψ ′ d x | 2 < ℏ 2 2 m | d ψ d x | 2 {\textstyle {\frac {\hbar ^{2}}{2m}}\left|{\frac {d\psi '}{dx}}\right|^{2}<{\frac {\hbar ^{2}}{2m}}\left|{\frac {d\psi }{dx}}\right|^{2}} everywhere because of the normalization. More significantly, the average kinetic energy is lowered by O (ε) {\displaystyle O(\varepsilon)} by the deformation to ψ '.