Hamiltonian of open string field theory for time-dependent solutions

Using the recently introduced expression for conserved charges of $L_\infty$ theories, we give an explicit form for the Hamiltonian of Witten's bosonic open string field theory. We evaluate it on the Erler-Maccaferri analytic solution, describing any D$p$-brane configuration associated to a BCFT. We use the expression to compute the energy of the rolling tachyon solution and find exact agreement with the boundary state result by Sen.