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In 1913 de Broglie was awarded his Licence ès Sciences but before his career had progressed much further World War I broke out. During the War de Broglie served in the army. He was attached to the wireless telegraphy section for the whole of the war and served in the station at the Eiffel Tower. During these war years all his spare time was spent thinking about technical problems. He explained how he was attracted to mathematical physics after the War (see for example ):

When in 1920 I resumed my studies ... what attracted me ... to theoretical physics was ... the mystery in which the structure of matter and of radiation was becoming more and more enveloped as the strange concept of the quantum, introduced by Planck in 1900 in his researches into black-body radiation, daily penetrated further into the whole of physics.

Taking up research in mathematical physics, de Broglie nevertheless maintained an interest in experimental physics. His brother Maurice de Broglie was at that time carrying out experimental work on X-rays and this proved a considerable interest to de Broglie during the first few years of the 1920s during which he worked for his doctorate. De Broglie's doctoral thesis Recherches sur la théorie des quanta (Researches on the quantum theory) of 1924 put forward this theory of electron waves, based on the work of Einstein and Planck . It proposed the theory for which he is best known, namely the particle-wave duality theory that matter has the properties of both particles and waves.

In a lecture de Broglie gave on the occasion when he received the Nobel Prize in 1929 he explained the background to the ideas contained in his doctoral thesis (see for example ):

Thirty years ago, physics was divided into two camps: ... the physics of matter, based on the concepts of particles and atoms which were supposed to obey the laws of classical Newtonian mechanics, and the physics of radiation, based on the idea of wave propagation in a hypothetical continuous medium, the luminous and electromagnetic ether. But these two systems of physics could not remain detached from each other: they had to be united by the formulation of a theory of exchanges of energy between matter and radiation. ... In the attempt to bring the two systems of physics together, conclusions were in fact reached which were neither correct nor even admissible when applied to the energy equilibrium between matter and radiation ... Planck ... assumed ... that a light source ... emits its radiation in equal and finite quantities - in quanta. The success of Planck 's ideas has been accompanied by serious consequences. if light is emitted in quanta, must it not, once emitted, possess a corpuscular structure? ... Jeans and Poincaré [showed] that if the motion of the material particles in a source of light took place according to the laws of classical mechanics, then the correct law of black-body radiation, Planck 's law, could not be obtained.

During an interview in 1963 de Broglie described how, given the above background, his discoveries came about:

As in my conversations with my brother we always arrived at the conclusion that in the case of X-rays one had both waves and corpuscles, thus suddenly - ... it was certain in the course of summer 1923 - I got the idea that one had to extend this duality to material particles, especially to electrons. And I realised that, on the one hand, the Hamilton - Jacobi theory pointed somewhat in that direction, for it can be applied to particles and, in addition, it represents a geometrical optics; on the other hand, in quantum phenomena one obtains quantum numbers, which are rarely found in mechanics but occur very frequently in wave phenomena and in all problems dealing with wave motion.

The wave nature of the electron was experimentally confirmed in 1927 by C J Davisson, C H Kunsman and L H Germer in the United States and by G P Thomson (the son of J J Thomson) in Aberdeen, Scotland. De Broglie's theory of electron matter waves was later used by Schrödinger , Dirac and others to develop wave mechanics.

After his doctorate, de Broglie remained at the Sorbonne where he taught for two years, becoming professor of theoretical physics at the Henri Poincaré Institute in 1928. From 1932 he was also professor of theoretical physics at the Faculté des Sciences at the Sorbonne. De Broglie taught there until he retired in 1962. From 1944 he was a member of the Bureau des Longitudes. In 1945 he became an adviser to the French Atomic Energy Commissariat.

His greatest honour was being awarded the Nobel Prize in 1929. We have quoted above from his lecture given at the award ceremony. Let us quote further from the lecture (see for example ):

Thus I arrived at the following general idea which has guided my researches: for matter, just as much as for radiation, in particular light, we must introduce at one and the same time the corpuscle concept and the wave concept. In other words, in both cases we must assume the existence of corpuscles accompanied by waves. But corpuscles and waves cannot be independent, since, according to Bohr, they are complementary to each other; consequently it must be possible to establish a certain parallelism between the motion of a corpuscle and the propagation of the wave which is associated with it.

After receiving the Nobel Prize in 1929 De Broglie worked on extensions of wave mechanics. Among publications on many topics he published work on Dirac's theory of the electron, on the new theory of light, on Uhlenbeck 's theory of spin, and on applications of wave mechanics to nuclear physics. He wrote at least twenty-five books including Ondes et mouvements (Waves and motions) (1926), La mécanique ondulatoire (Wave mechanics) (1928), Une tentative d'interprétation causale et non linéaire de la mécanique ondulatoire: la théorie de la double solution (1956), Introduction à la nouvelle théorie des particules de M Jean-Pierre Vigier et de ses collaborateurs (1961), Étude critique des bases de l'interprétation actuelle de la mécanique ondulatoire (1963). The last three mentioned books were published in English translations as Non-linear Wave Mechanics: A Causal Interpretation (1960), Introduction to the Vigier Theory of elementary particles (1963), and The Current Interpretation of Wave Mechanics: A Critical Study (1964).

He wrote many popular works which demonstrate his interest in the philosophical implications of modern physics, including Matter and Light: The New Physics (1939); The Revolution in Physics (1953); Physics and Microphysics (1960); and New Perspectives in Physics (1962).

In 1933 de Broglie was elected to the Académie des Sciences becoming Permanent Secretary for the mathematical sciences in 1942. The Académie awarded him its Henri Poincaré Medal in 1929 and the Albert I of Monaco Prize in 1932. Other honours which he received included the Kalinga Prize which was awarded to him by UNESCO in 1952 for his efforts towards the understanding of modern physics by the general public. The French National Scientific Research Centre awarded him its gold medal in 1956. Further honours included the awarding of the Grand Cross of the Légion d'Honneur and Belgium made him an Officer of the Order of Leopold. He received honorary doctorates from the Universities of Warsaw, Bucharest, Athens, Lausanne, Quebec, and Brussels. He was elected to honorary membership of eighteen academies and learned societies in Europe, India, and the United States.

De Broglie described himself as:

... having much more the state of mind of a pure theoretician than that of an experimenter or engineer, loving especially the general and philosophical view ... .

The central question in de Broglie's life was whether the statistical nature of atomic physics reflects an ignorance of the underlying theory or whether statistics is all that can be known. For most of his life he believed the former although as a young researcher he had at first believed that the statistics hide our ignorance. Perhaps surprisingly, he returned to this view late in his life stating that:

... the statistical theories hide a completely determined and ascertainable reality behind variables which elude our experimental techniques.

Let us end our biography with the tribute paid to de Broglie by C W Oseen, Chairman of the Nobel Committee for Physics of the Royal Swedish Academy of Sciences :

When quite young you threw yourself into the controversy raging round the most profound problem in physics. You had the boldness to assert, without the support of any known fact, that matter had not only a corpuscular nature, but also a wave nature. Experiment came later and established the correctness of your view. You have covered in fresh glory a name already crowned for centuries with honour.

Source:School of Mathematics and Statistics University of St Andrews, Scotland