Quantum phase shift of spatially confined de Broglie waves in a gravitational field

Luca D’Errico, Elmo Benedetto, A. Feoli

D. A. L. Paul

The dispersion relation for de Broglie waves is examined sufficiently to remove a possible ambiguity in the de Broglie frequency. The motion of a heavy (guided) photon, which obeys the same dispersion relation, is then studied in a gravitational field, leading to the Einsteinian relation frequency shift in a gravitational field.

Luca D’Errico

Jonáš Kulhánek

Aditya Guleria

This work presents a theoretical formulation describing how the de Broglie wavelength of a particle changes when the particle moves through a spatially dependent force field. By combining the de Broglie relation with the classical work–energy theorem, a general expression is derived for the wavelength shift caused by the work performed by an arbitrary force field. The model establishes a simple analytical connection between classical mechanics and quantum wave behavior. The derived expression shows that the shift in matter-wave wavelength depends directly on the work done by external forces. A weak-field approximation is also developed, providing a simplified relation between wavelength shift and the applied force. Example calculations and graphical predictions are presented to illustrate the theoretical behavior of the model. The framework may have applications in systems involving matter-wave propagation under external potentials, such as charged particles in electric fields, gravitational potentials, and other spatially varying force environments. This work aims to provide an intuitive analytical perspective on how classical forces influence quantum wave properties and may serve as a starting point for further theoretical investigations in matter-wave physics.

Samuel A. Werner

Experiments involving quantum interference of neutron de Broglie waves, having a wavelength A , extending over macroscopic distances of order are described. In particular I discuss interference induced by the Earth's gravitational field and by its rotation (Sagnac effect), the topological phase shifts resulting from the diffraction of the neutron, carrying its magnetic moment , around a charged electrode (Aharonov--Casher effect) and then finally during its passage through a pulsed magnetic field (scalar Aharonov--Bohm effect).