Our ninth most important physics publication comes from 1926, when the basic formulation of quantum mechanics was laid down by Erwin Schrodinger in the paper An Undulatory Theory of the Mechanics of Atoms and Molecules[1].

The paper is the culmination of Schrodinger’s work, and that of his contemporaries, to expand upon Louis de Broglie’s dissertation, which associated a wavelength with massive particles. Other papers were published in German prior to this one [2], but unfortunately I can’t read German, and this paper is a summary of results.

The paper’s approach to quantum mechanics is an interesting one, beginning with the Hamilton-Jacobi principle and obtaining a differential equation second order in the coordinates and first order in time. He then postulates the stationary state wave function of the form, and correctly identifies Planck’s constant as the correct quantum unit of action. Schrodinger even had the insight to identify the momentum and position coordinates of classical mechanics with the terms in his wave equation.

The paper also includes the established results of Max Born’s statistical interpretation of the wave function, illustrating that this exact paper is more a summary of half a decade of work than it is one single piece of intellectual contribution.

Nevertheless, the paper is interesting to me for several reasons. The paper attempts to provide a good deal of physical insight, frequently appealing to the experimental work of others, and comparing his results to the theoretical work of those before. It is clear that this paper was Schrodinger’s attempt to have his theory generally accepted, and he very clearly illustrates the strong points of his work. This is not unusual — part of writing a physics paper is tooting your own horn. But in the paper, Schrodinger even acknowledges that “after the main features of undulatory mechanics had been developed, its complete mathematical agreement with the theory of matrices put forward by Heisenberg, Born and Jordan [3]” was confirm. Schrodinger even acknowledges that his theory is, interestingly enough, not the only correct representation. The notion of matrix mechanics eventually took hold, but its agreement with Schrodinger’s results was crucial for this development.

This paper, and the work leading up to and included in it, set the stage for half of twentieth century physics, and the results are now standard knowledge for every physicist. For these reasons, the introduction of the wave equation deserves a spot on this list.

[1] Schrodinger, E. “An Undulatory Theory of the Mechanics of Atoms and Molecules”. Phys. Rev. 28, 6.

[2] The paper, published in Annalen der Physik was entitled “Quantisierung als Eigenwertproblem”, which translates as “Quantization of the Eigenvalue Problem”. In papers that rapidly followed, Schrodinger gave correct energy levels for the hydrogen atom, the harmonic oscillator, provided a treatment of the Stark effect, and gave a treatment of scattering. These results are, for the most part, summarized in [1].

[3] There are a long series of papers by Jordan, Heisenberg, Born, Dirac and Pauli all discussing matrix mechanics and its connection with wave mechanics. Of course, of the list of people here, only Paul Jordan did not win a Nobel Prize eventually.