Inertial and gravitational mass in quantum mechanics

TL;DR

This paper investigates how inertial and gravitational masses influence quantum wave packets in a gravitational field, revealing mass ratios affect dynamics and energy spectra, which could enable quantum tests of free fall universality.

Contribution

It demonstrates the dependence of quantum wave packet dynamics and energy spectra on mass ratios, providing new insights into quantum tests of the equivalence principle.

Findings

Wave packet dynamics depend on the ratio of gravitational to inertial mass.

Energy spectrum depends on the masses with fractional powers.

Potential for quantum experiments testing free fall universality.

Abstract

We show that in complete agreement with classical mechanics, the dynamics of any quantum mechanical wave packet in a linear gravitational potential involves the gravitational and the inertial mass only as their ratio. In contrast, the spatial modulation of the corresponding energy wave function is determined by the third root of the product of the two masses. Moreover, the discrete energy spectrum of a particle constrained in its motion by a linear gravitational potential and an infinitely steep wall depends on the inertial as well as the gravitational mass with different fractional powers. This feature might open a new avenue in quantum tests of the universality of free fall.