September 2023 marked the centenary of “Ondes et quanta”, a paper in which French physicist Louis de Broglie proposed that matter is associated with a wave motion, and which ultimately won him the 1929 Nobel Prize for Physics.
Where did we get that [equation] from? Nowhere. It is not possible to derive it from anything you know. It came out of the mind of Schrödinger. Richard Feynman De Broglie's matter waves The early struggles of physicists towards a quantum theory were mostly concerned with attempts to understand the nature of light. The traditional picture of light as a wave motion had been challenged by Planck and Einstein. They had shown that certain experimental results that were impossible to understand in terms of a wave picture could be easily explained if light was thought of as a stream of particles, now called photons. William Bragg, who, with his son, won the 1915 Nobel Prize for studies of crystal structure using X-rays, summarized this dilemma for physics by exclaiming in despair that he was teaching the corpuscular theory of light on Mondays, Wednesdays and Fridays, and the undulatory theory on Tuesdays, Thursdays and Saturdays! Physicists were still wrestling with these apparently contradictory properties of light when, in 1924, Prince Louis de Broglie (pronounced ‘de Broy’) suggested that all matter, even objects that we usually think of as particles – such as electrons – should also display wavelike behaviour! This revolutionary idea was completely unexpected and, what is more, was included by de Broglie in his Ph. D. thesis. Like most people, physicists are generally reluctant to accept any wild new idea, especially if there is not a shred of evidence to support it.
Background At a time when no single known fact supported this theory, Louis de Broglie asserted that a stream of electrons which passed through a very small hole in an opaque screen must exhibit the same phenomena as a light ray under the same conditions. (Prof. C. W. Oseen, Chairman of the Nobel Committee for Physics, presentation speech, 12 December 1929 (Oseen 1999)) In September 1923, Prince Louis de Brogliea made one of the most astonishing predictions in the history of theoretical physics: that material bodies would exhibit the wave-like phenomena of diffraction and interference upon passing through sufficiently narrow slits. Like Einstein's prediction of the deflection of light by the sun, which was based on a reinterpretation of gravitational force in terms of geometry, de Broglie's prediction of the deflection of electron paths by narrow slits was made on the basis of a fundamental reappraisal of the nature of forces and of dynamics. De Broglie had proposed that Newton's first law of motion be abandoned, and replaced by a new postulate, according to which a freely moving body follows a trajectory that is orthogonal to the surfaces of equal phase of an associated guiding wave. The resulting ‘de Broglian dynamics’ – or pilot-wave theory as de Broglie later called it – was a new approach to the theory of motion, as radical as Einstein's interpretation of the trajectories of falling bodies as geodesics of a curved spacetime, and as far-reaching in its implications. In 1929 de Broglie received the Nobel Prize ‘for his discovery of the wave nature of electrons’.