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Thus Weyl’s law actually has its roots in acoustics. In view of the fact that Rayleigh was a leading expert in acoustics and the author of the famous book “The Theory of Sound” [27], ﬁrst published in 1877, it is not surprising that he realized that the radiation problem can be related to the number of vibrational modes of a black body cavity. 19). The problem was of course a question of the correct boundary conditions in the electromagnetic case. In his book, Rayleigh writes: “Some of the natural notes of the air contained within a room may generally be detected on singing the scale.

In 1908 he founded modern chaos theory in his book Science et méthode by suggesting that “it may happen that small differences in the initial conditions produce very great ones in the ﬁnal phenomena”. Probably Albert Einstein was the ﬁrst to come into touch with the question of whether chaos plays a role in the realm of quantum mechanics, in 1917. However, a systematic approach towards the chaotic behavior in atomic and subatomic systems was only initiated by Eugene Wigner in 1951. A striking connection between the eigenvalues of the Schrödinger operator and classical dynamics had been observed by Martin Gutzwiller in 1971.

Then he continues: “When we pass from one dimension to three dimensions, and consider for example the vibrations of a cubic mass of air, we have (‘Theory of Sound’, paragraph 267) as the equation for ν2 , ν2 = p2 + q2 + r2 , where p, q, r are integers representing the number of subdivisions in the three directions. If we regard p, q, r as the coordinates of points forming a cubic array, ν is the distance of any point from the origin. Accordingly the number of points for which ν lies between ν and ν + dν, proportional to the volume of the corresponding spherical shell, may be represented by ν2 dν, and this expresses the distribution of energy according to the Boltzmann–Maxwell law, so far as regards the wavelength or frequency.