252 
THE QUANTUM [xvm. 4 
As we have seen Schrodinger starts from the idea suggested 
by de Broglie that an atomic system is not to be represented by 
a trajectory, i.e., by a point moving through the co-ordinate 
space but must be represented by a wave in this space. From 
this starting-point he develops a wave-theory of matter, and 
obtains from a variation principle a differential equation which 
the wave function must satisfy. This equation turns out to be 
closely connected with the Hamiltonian dynamical equation 
which specifies the system. When the general solution of this 
equation is known, matrices to represent the canonical variables 
may easily be obtained satisfying all the conditions that they 
have to satisfy according to Heisenberg’s matrix mechanics. 
The mathematical equivalence of the theories is thus established, 
and it is shown that, in the words of Schrodinger, “ the wave- 
mechanics and the matrix mechanics are mathematically 
identical.” The concept of characteristic oscillations in the 
atom and Schrodinger’s theory based upon it represent a most 
significant contribution to the development of the quantum 
theory. “ From the formal mathematical point of view it 
includes the whole of the Heisenberg-Born-Dirac matrix theory 
and gives, moreover, a simplified, practically convenient method 
of finding the matrices. Beyond this, it opens new avenues of 
thought and seems to afford our first glimpse of the true nature 
of the quanta ” (Epstein). 
Although it is impossible in a single paragraph to do justice 
to the important work of A. N. Whitehead,* some reference must 
be made to it here because of the close relationship it bears to 
the theories advanced in this volume and in particular to the 
new undulatory mechanics. Whitehead has developed what he 
calls the organic theory of nature : a complete organism in the 
organic theory corresponds to a bit of material on the materialistic 
theory. A primate may be described briefly as a primary organism 
which is not decomposable into subordinate organisms. “ There 
are certain indications in modern physics that for the role of 
corpuscular organisms at the base of the physical field, we 
require vibratory entities. Such corpuscles would be the 
corpuscles detected as expelled from the nuclei of atoms, which 
then dissolve into waves of light.” “ A proton, and perhaps an 
electron, would be an association of such primates, superposed 
on each other, with their frequencies and spatial dimensions so 
arranged as to promote the stability of the complex organism, 
when jolted into acceleration of locomotion.” The conception 
may be made clearer by means of an analogy from sound or from 
* A. N. Whitehead, The Concept of Nature ; An Enquiry concerning 
the Principles of Natural Knowledge ; Science and the Modern World (Chap. 
VIII, “ The Quantum Theory ”) ; Cambridge University Press.