The third way to quantum mechanics is the forgotten first

TL;DR

This paper uncovers a forgotten early formulation of quantum mechanics by Gregor Wentzel, highlighting its foundational role and its influence on Feynman's later work, despite initial neglect and limitations.

Contribution

The paper reveals Wentzel's overlooked formulation of quantum mechanics predating Feynman, emphasizing its historical significance and foundational contribution.

Findings

Wentzel's work predates Feynman's formulation.

Wentzel's approach was initially rejected and considered naive.

Feynman's work validated Wentzel's foundational ideas.

Abstract

Quantum mechanics can be formulated in three ways, as Heisenberg, Schr\"odinger and Feynman did respectively. For the last way, an unknown (i.e. forgotten) forerunner exists, that we have found in a paper by Gregor Wentzel, published before the famous works by Heisenberg and Schr\"odinger, and contemporary with the fundamental works of L. de Broglie. In that paper, one can find the basic formulae and their interpretation as they were adopted by Feynman twenty years later. We believe that Wentzel's work was forgotten for several reasons: (I) Schr\"odinger's equation was much simpler to deal with (Wentzel himself contributed to its development in the same way as L.Brillouin and H.Kramers did). (II) The first application was rejected by Heisenberg and Kramers. (III) The approximation used by Wentzel was too na\"\i ve and failed. Nevertheless, the foundation laid by Wentzel was sound, as it has been shown by Feynman's work. Therefore, Wentzel has to be considered as one of the founders of quantum mechanics.