Hydrogen atom wave function and eigen energy in the Rindler space

TL;DR

This paper investigates how the hydrogen atom's wave function and energy levels are affected in Rindler space, revealing tilted probability distributions and potential ionization at extremely high accelerations.

Contribution

It introduces the analysis of hydrogen atom eigenstates in Rindler space, highlighting the effects of acceleration on wave functions and energy levels, including ionization phenomena.

Findings

Wave function probability distribution is tilted in Rindler space.

Electrons can tunnel and ionize at accelerations around 3×10^22 m/s^2.

Ionization occurs due to electromagnetic effects under high acceleration.

Abstract

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.