Doppler Shift of the de Broglie Waves- Some New Results from Very Old Concepts

TL;DR

This paper derives the Doppler shift for de Broglie waves of fermions and bosons using Lorentz transformations and explores how their wavelength varies with temperature in many-body quantum gases.

Contribution

It introduces a formalism to analyze the temperature dependence of de Broglie wavelengths in Fermi and Bose gases based on classical Wien's idea.

Findings

Doppler shift formulas for de Broglie waves of fermions and bosons.

Temperature-dependent variation of de Broglie wavelengths in quantum gases.

Application of Lorentz transformations to quantum wave phenomena.

Abstract

The Doppler shift of de Broglie wave is obtained for fermions and massive bosons using the conventional form of Lorentz transformations for momentum and energy of the particles. A formalism is developed to obtain the variation of wave length for de Broglie waves with temperature for individual particles using the classic idea of Wien in a many body Fermi gas or massive Bose gas.