Correct normalization of phonon modes for Rayleigh waves.

Abstract

Phonon mode normalizations derived in this paper are based on a consistent approach for normalizing Rayleigh waves. These Rayleigh waves are being used increasingly for nanoscale applications, including quantum information technology, and currently the literature is full of unnecessary approximate forms of these normalizations. The self-consistency of these derivations, for commonly used Rayleigh wave modes, is based on the second quantization procedure where the mechanical energy in the modes is equated with the energy of a phonon mode.