236 ANNUAL REPORT SMITHSONIAN INSTITUTION, 19 3 



chanical models that had been proposed and to develop a mathe- 

 matical theory of the atom which would involve only concepts that 

 were definable in terms of operations. That is, the theory was one 

 that dealt more directly with measurable quantities such as the 

 frequencies of spectral lines. New methods of matrix calculus had 

 to be evolved, a kind of calculus of discontinuities or discrete quan- 

 tities instead of the calculus of continuous quantities which had 

 characterized classical mechanics. 



Only a little later Schroedinger, by developing De Broglie's wave 

 theory of quantum phenomena, was able to build up a theory that 

 we will now refer to as the wave mechanics, according to which 

 the whole atom with all its electrons can be looked upon as a wave 

 phenomenon. The electrons are no longer considered to be moving 

 in orbits. For example, the hydrogen atom is found to have spheri- 

 cal symmetry instead of the axial symmetry of the old Bohr model 

 of the atom. Yet this theory leads to identically the same equations 

 for the frequencies of the lines in the hydrogen spectrum. We must 

 not say that Bohr's theory of the hydrogen atom has been over- 

 thrown. Bohr's TTiechanical model has been superseded, but the 

 more important model which is represented by the equations and 

 the concepts which he evolved is even better to-day than it was 

 when it was first proposed. 



The wave mechanics which involves the calculus of continuous 

 variables is not now in conflict with the Bohr matrix calculus of 

 discrete quantities. The two theories are essentially merely different 

 mathematical methods applied to a single fundamental problem. 

 The resulting mathematical equations alwa3's agree with one another. 

 One begins to believe that the mathematical theory is a far better 

 model of the atom than any of the mechanical models which are 

 possible. 



The long-standing conflict between the wave theory of light and the 

 corpuscular quantum theor}'^ now disappears with the new wave 

 mechanics, the two aspects of light being somewhat analogous to the 

 two aspects of the quantum theory, the wave mechanics and the 

 matrix mechanics. In fact, the quantum theory now indicates that 

 the electron itself can be regarded as a particle, or as a wave, just 

 as light can be thought of as a photon or a wave. Whatever re- 

 mained of the conflict between the wave and corpuscular theory of 

 light and of the electron seems now to be fundamentally removed 

 by the Bohr-Heisenberg uncertainty principle. To ask whether 

 an electron is a particle or a wave is a meaningless question ; the same 

 is true of the question whether light consists of corpuscles or waves. 

 One must answer that both of these are particles or waves accord- 

 ing to the kind of operations that we may perform in observing 



