# Schroedinger Correspondence Applied to Crystals

## TL;DR

This paper discusses Schroedinger's 1926 work on wave packets in harmonic oscillators, highlighting a novel correspondence principle that links quantum states to classical motion, with applications to harmonic solids.

## Contribution

It extends Schroedinger's correspondence principle to N-dimensional harmonic oscillators, offering a new approach to analyze harmonic solids and anharmonic effects.

## Key findings

- Schroedinger's wave packets follow classical equations of motion.
- The correspondence principle applies to multi-dimensional oscillators.
- Potential applications to anharmonic corrections in solids.

## Abstract

In 1926, E. Schroedinger published a paper solving his new time dependent wave equation for a displaced ground state in a harmonic oscillator (now called a coherent state). He showed that the parameters describing the mean position and mean momentum of the wave packet obey the equations of motion of the classical oscillator while retaining its width. This was a qualitatively new kind of correspondence principle, differing from those leading up to quantum mechanics. Schroedinger surely knew that this correspondence would extend to an N-dimensional harmonic oscillator. This Schroedinger Correspondence Principle is an extremely intuitive and powerful way to approach many aspects of harmonic solids including anharmonic corrections.