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Volume 14: Pages 248-254, 2001

Wave Equations for Atoms and Molecules under the Action of Gravity

Jair Lucinda

Departamento de Física, Universidade Federal do Paraná, CP 19044, CEP 81531‐990, Curitiba, Paraná, Brazil

There is an increasing interest in experiments with microgravity in quantum systems. However, there is no satisfactory theoretical procedure merging quantum mechanics and the geometric approach to gravity. Here, we obtain the effect of gravity on atomic and molecular spectra within a framework in which the unification of space and time also takes into account the difference in gravitational potential between frames of reference. Maintaining only effects due to the relativistic nature of gravitational interaction, we obtain a relation that leads to a modified Schrödinger equation for an electron bound to an atomic nucleus. The solution of this modified wave equation gives the gravitational redshift (or blueshift) of frequency as a relativistic effect of gravity on atomic internal energy levels. Finally, with a similar procedure, we obtain wave equations that give the effect of gravitational interaction on the rotation and vibration spectra of diatomic molecules. All results are in agreement with the “slowing‐down” effect of gravity on frequency standards.

Keywords: Schrödinger equation, diatomic molecule, gravitational redshift, molecular spectrum, atomic spectrum, gravity

Received: September 19, 2000; Published online: December 15, 2008