  The near-term search for life beyond the solar system currently focuses on
transiting planets orbiting small M dwarfs, and the challenges of detecting
signs of life in their atmospheres. However, planets orbiting white dwarfs
(WDs) would provide a unique opportunity to characterize rocky worlds. The
discovery of the first transiting giant planet orbiting a white dwarf, WD
1856+534b, showed that planetary-mass objects can survive close-in orbits
around WDs. The large radius ratio between WD planets and their host renders
them exceptional targets for transmission spectroscopy. Here, we explore the
molecular detectability and atmospheric characterization potential for a
notional Earth-like planet, evolving in the habitable zone of WD 1856+534, with
the James Webb Space Telescope (JWST). We establish that the atmospheric
composition of such Earth-like planets orbiting WDs can be precisely retrieved
with JWST. We demonstrate that robust > 5$\sigma$ detections of H$_2$O and
CO$_2$ can be achieved in a 5 transit reconnaissance program, while the
biosignatures O$_3$ + CH$_4$, and O$_3$ + N$_2$O can be detected to > 4$\sigma$
in as few as 25 transits. N$_2$ and O$_2$ can be detected to > 5$\sigma$ within
100 transits. Given the short transit duration of WD habitable zone planets (~
2 minutes for WD 1856+534), conclusive molecular detections can be achieved in
a small or medium JWST transmission spectroscopy program. Rocky planets in the
WD habitable zone therefore represent a promising opportunity to characterize
terrestrial planet atmospheres and explore the possibility of a second genesis
on these worlds.
