276 Chapter 18
In his later presentations of his argument (beginning with the second installment of
his 1926 papers), Schr ö dinger characteristically brought forward the optical version of
his analogy, in which he connected acoustics and optics with mechanics through an
analogy with the Hamilton – Jacobi equation of dynamics. Given his visual bent, it is not
surprising that, in those later presentations, he tended to describe his equation in optical
language, using concepts like rays: lecturing on his theory in 1928, he opined that “ Ham-
ilton ’ s wave-picture, worked out in the way discussed above, contains something that
corresponds to ordinary mechanics, namely, the rays correspond to the mechanical paths ,
and signals move like mass-points. ”^11 Nevertheless, in his very first 1926 presentation
of the nascent theory, Schr ö dinger did not use this optical language but instead spoke
only of vibrating strings. He even found himself in the curious situation of trying to
express optics in terms of sound, not just by analogy (as had Euler and Young) but
somehow more literally and directly, invoking the sonic difference tones introduced by
Helmholtz:Figure 18.2
An illustration of the orbits of electrons in the Bohr – Sommerfeld theory for various elements, from H. A. Kramers
and Helge Holst, The Atom and the Bohr Theory of Its Structure (1923).