  Time-dependent calculation has been a suitable method to investigate the
quantum dynamical processes. In Ref. [1] = [T. Oishi et al., J. of Phys. G 45,
105101 (2018)], we applied this method to the one-dimensional two-fermion
tunneling in the nuclear-physics scale. Beside the specific results presented
therein, some basic formalism and methods, which can be helpful for further
discussions and developments to investigate time-dependent quantum systems,
have been awaiting our description. This note is devoted to describe those
supplemental contents. We do not limit the story to the nuclear physics, but
keep it applicable to other scales and/or targets.
