 Frequency-regulated Dirichlet Casimir energy

For a massless real scalar in one spatial dimension, applying $e^{-\omega /(\pi \Lambda )}$ to both the Dirichlet mode sum and the unbounded-line integral gives the same leading bulk energy $\pi L{\Lambda }^2/2$. Their finite difference is $-\pi /(24L)$ in units $\hslash =c=1$, producing the attractive force $-\pi /(24L^2)$. This scalar boundary force is distinct from the retarded atom-surface Casimir-Polder interaction.