The Energy-Level Shifts of a Stationary Hydrogen Atom in Static External Gravitational Field with Schwarzschild Geometry

TL;DR

This paper calculates the first-order energy shifts of various hydrogen atom levels in a Schwarzschild gravitational field, revealing specific patterns related to angular momentum quantum numbers that could help distinguish gravitational effects.

Contribution

It provides the first detailed calculation of relativistic energy-level shifts of hydrogen in a static gravitational field with Schwarzschild geometry, highlighting unique angular momentum patterns.

Findings

Energy shifts for states with total angular momentum 1/2 are zero.

The ratio of energy shifts for states with total angular momentum 5/2 is 1:4:5.

The results can help differentiate gravitational effects from other influences.

Abstract

The first order perturbations of the energy levels of a stationary hydrogen atom in static external gravitational field, with Schwarzschild metric, are investigated. The energy shifts are calculated for the relativistic 1S, 2S, 2P, 3S, 3P, 3D, 4S, 4P, 4D and 4F levels. The results show that the energy-level shifts of the states with total angular momentum quantum number 1/2 are all zero, and the ratio of absolute energy shifts with total angular momentum quantum number 5/2 is 1:4:5. This feature can be used to help us to distinguish the gravitational effect from other effect.