Schrödinger Correspondence Applied to Crystals


Heller, E.J. & Kim, D. Schrödinger Correspondence Applied to Crystals. J. Phys. Chem. A (2019).


In 1926, E. Schrödinger 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. Schrödinger surely knew that this correspondence would extend to an N-dimensional harmonic oscillator. This Schrödinger Correspondence Principle is an extremely intuitive and powerful way to approach many aspects of harmonic solids including anharmonic corrections.

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