Schrödinger Correspondence Applied to Crystals.

In 1926, E. Schrödinger showed that the mean position and mean momentum of the displaced ground state in a harmonic oscillator obey the equations of motion of the classical oscillator. This Schrödinger Correspondence Principle, extended to an N-dimensional harmonic oscillator, is an intuitive and powerful way to approach many aspects of harmonic solids by converting the quantum-mechanical problems to the classical ones. For the application of the correspondence principle, the concepts of the phonon and its pseudomomentum are clarified, and the importance of taking into account the center-of-mass momentum is explained. Also, the concept of the antiphonon is introduced through the examples of physical processes in a line and a ring of atoms. With the correspondence principle, the quantum behavior of harmonic solids under a Mössbauer-like kick is analyzed classically, and the simulation verified the formation of an antiphonon.