  We study the hydrogen atom eigenstate energy and wave function in the Rindler
space. The probability distribution is tilted because the electric field of the
nucleus is no longer spherically symmetric. The hydrogen atom therefore cannot
be treated exactly in the same way as what it is in an inertial frame. We also
find that if the external force accelerates only the nucleus and then the
nucleus accelerates its surrounding electrons through electromagnetic force,
the electrons can tunnel through the local energy gap and split the hydrogen
atom into an ion. This is similar to what one expects from the Stark effect.
However, the critical acceleration is about $3\times 10^{22} m/s^2$. It is well
beyond the gravitational acceleration on a regular star surface.
