By 1900, it was known that atomic energy levels are discrete. It was also known that the specific heat of solid decreases drastically for low temperature. In 1906, Einstein worried about these problems and decided to try discrete energy levels for solid. He did an exercise problem assuming that energy levels in solid are equal-spaced. This was the simplest model one can think of for discrete energy levels. Did Einstein know that this equal-spacing has anything to do with harmonic oscillators? Quantum mechanics was not formulated until 1927.

Indeed, many people imitated Einstein. Here is a photo of those who used harmonic oscillators to invent new theories.

The original version of Einstein's formula for specific heat is still used for vibrational modes of molecular excitations. However, his formula fails to describe the T³ behavior as T approaches zero.

In 1912, a Dutch physicist/chemist named Petrus Josephus Wilhelmus Debye introduced the concept of phonons for acoustic waves in solid by imitating Einstein's photons based on light waves. Debye then derived the specific heat of solid which produces correctly the T³ behavior. The Debye formula can be found in standard textbooks on statistical mechanics and webpages like http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/debye.html. These days, we cannot do condensed matter physics without phonons.

People wonder why Einstein did not get Nobel prize for his formulation of relativity. I am not against Debye's 1936 Nobel prize in chemistry, but I wonder why he did not get a Nobel in physics for his phonons.

Let us go back to harmonic oscillators. In addition to the items which I mentioned in one of my earlier articles, harmonic oscillators form the basis for second quantization and the Fock space. In quantum optics, both coherent and squeezed states are harmonic-oscillator states. Atomic and Molecular physics is largely a physics of harmonic oscillators. Harmonic oscillators serve as essential instruments in physics teaching. In short, modern physics is a physics of harmonic oscillators, as Einstein noted in 1906.

Y. S. Kim (2006.1.18)

Date: Wed, 18 Jan 2006 15:57:57 +0600
From: Arkadii Kozhevnikov

Dear Prof. Kim,

You have arranged six nice photos on Einstein's 1906 web page. But I wonder why Planck's photo is absent? He used harmonic oscillator in his studies of blackbody radiation resulted in inventing quantum theory.

Yours sincerely,

A. A. Kozhevnikov