1929 L DE BROGLIE to the fine work done by Schrodinger. It is based on wave propagation equations and strictly defines the evolution in time of the wave associated with a corpuscle. It has in particular succeeded in giving a new and more satisfactory form to the quantization conditions of intra-atomic motion since he classical quantization conditions are justified, as we have seen, by the pplication of geometrical optics to the waves associated with the intra atomic corpuscles, and this application is not strictly justified I cannot attempt even briefly to sum up here the development of the new mechanics. I merely wish to say that on examination it proved to be iden- tical with a mechanics independently developed, first by Heisenberg, then by Born, Jordan, Pauli, Dirac, etc. quantum mechanics. The two mechan- ics, wave and quantum, are equivalent from the mathematical point of vIew We shall content ourselves here by considering the general significance of the results obtained. To sum up the meaning of wave mechanics it can be stated that: "A wave must be associated with each corpuscle and only the study of the waves propagation will yield information to us on the succes sive positions of the corpuscle in space". In conventional large-scale mechani cal phenomena the anticipated positions lie along a curve which is the trajec- tory in the conventional meaning of the word. But what happens if the wave does not propagate according to the laws of optical geometry, if, say, there are interferences and diffraction? Then it is no longer possible to assign to the corpuscle a motion complying with classical dynamics, that much is certain Is it even still possible to assume that at each moment the corpuscle occupies a well-defined position in the wave and that the wave in its propagation car ries the corpuscle along in the same way as a wave would carry along a cork? These are difficult questions and to discuss them would take us too far and even to the confines of philosophy. All that I shall say about them here is that nowadays the tendency in general is to assume that it is not constantly pos- the corpuscle a well-defined position in the wave. I must restrict myself to the assertion that when an observation is carried out en abling the localization of the corpuscle, the observer is invariably induced to assign to the corpuscle a position in the interior of the wave and the the square of the amplitude, that is to say the intensity al proportional to probability of it being at a particular point M of the wave is This may be expressed in the following If we consider a cloud of corpuscles associated with the same wave, the intensity of th e wave at ea point is proportional to the cloud density at that point(ie to the number of252 1929 L.DE BROGLIE to the fine work done by Schrödinger. It is based on wave propagation equations and strictly defines the evolution in time of the wave associated with a corpuscle. It has in particular succeeded in giving a new and more satisfactory form to the quantization conditions of intra-atomic motion since the classical quantization conditions are justified, as we have seen, by the application of geometrical optics to the waves associated with the intra￾atomic corpuscles, and this application is not strictly justified. I cannot attempt even briefly to sum up here the development of the new mechanics. I merely wish to say that on examination it proved to be iden￾tical with a mechanics independently developed, first by Heisenberg, then by Born, Jordan, Pauli, Dirac, etc.: quantum mechanics. The two mechan￾ics, wave and quantum, are equivalent from the mathematical point of view. We shall content ourselves here by considering the general significance of the results obtained. To sum up the meaning of wave mechanics it can be stated that: "A wave must be associated with each corpuscle and only the study of the wave’s propagation will yield information to us on the succes￾sive positions of the corpuscle in space". In conventional large-scale mechani￾cal phenomena the anticipated positions lie along a curve which is the trajec￾tory in the conventional meaning of the word. But what happens if the wave does not propagate according to the laws of optical geometry, if, say, there are interferences and diffraction? Then it is no longer possible to assign to the corpuscle a motion complying with classical dynamics, that much is certain. Is it even still possible to assume that at each moment the corpuscle occupies a well-defined position in the wave and that the wave in its propagation car￾ries the corpuscle along in the same way as a wave would carry along a cork? These are difficult questions and to discuss them would take us too far and even to the confines of philosophy. All that I shall say about them here is that nowadays the tendency in general is to assume that it is not constantly pos￾sible to assign to the corpuscle a well-defined position in the wave. I must restrict myself to the assertion that when an observation is carried out en￾abling the localization of the corpuscle, the observer is invariably induced to assign to the corpuscle a position in the interior of the wave and the probability of it being at a particular point M of the wave is proportional to the square of the amplitude, that is to say the intensity at M. This may be expressed in the following manner. If we consider a cloud of corpuscles associated with the same wave, the intensity of the wave at each point is proportional to the cloud density at that point (i.e. to the number of