Localization length at a step Dirac mass wall (${\xi }_{\pm }=\hslash c/|V_{\pm }|$)

When the mass is constant $V_{+}>0$ above the wall and $V_{-}<0$ below it, amplitude decay lengths are ${\xi }_{+}=\hslash c/V_{+}$ and ${\xi }_{-}=\hslash c/|V_{-}|$. A scalar transverse envelope multiplying a unit spinor has normalization $\sqrt{2/({\xi }_{+}+{\xi }_{-})}$. Density decays twice as fast as amplitude.