  Following the discovery of the first exoplanet candidate transiting a white
dwarf (WD), a "white dwarf opportunity" for characterizing the atmospheres of
terrestrial exoplanets around WDs is emerging. Large planet-to-star size ratios
and hence large transit depths make transiting WD exoplanets favorable targets
for transmission spectroscopy - conclusive detection of spectral features on an
Earth-like planet transiting a close-by WD can be achieved within a medium
James Webb Space Telescope (JWST) program. Despite the apparently promising
opportunity, however, the post-main sequence (MS) evolutionary history of a
first-generation WD exoplanet has never been incorporated in atmospheric
modeling. Furthermore, second-generation planets formed in WD debris disks have
never been studied from a photochemical perspective. We demonstrate that
transmission spectroscopy can identify a second-generation rocky WD exoplanet
with a thick ($\sim1$ bar) H$_2$-dominated atmosphere. In addition, we can
infer outgassing activities of a WD exoplanet based on its transmission spectra
and test photochemical runaway by studying CH$_4$ buildup.
