OUTLINE OF SCHRODINGER'S THEORY 213 



be what we call potential energy, since it originates from 

 influences attributable to the presence of surrounding 

 objects. 



Assuming that we know both the real v and the 

 spurious or potential v for our ripples, the equation of 

 wave-propagation is settled, and we can proceed to solve 

 any problem concerning wave-propagation. In particular 

 we can solve the problem as to how the stormy areas 

 move about. This gives a remarkable result which 

 provides the first check on our theory. The stormy 

 areas (if small enough) move under precisely the same 

 laws that govern the motions of particles in classical 

 mechanics. The equations for the motion of a wave- 

 group with given frequency and potential frequency are 

 the same as the classical equations of motion of a par- 

 ticle with the corresponding energy and potential energy. 



It has to be noticed that the velocity of a stormy area 

 or group of waves is not the same as the velocity of an 

 individual wave. This is well known in the study of 

 water-waves as the distinction between group-velocity 

 and wave-velocity. It is the group-velocity that is ob- 

 served by us as the motion of the material particle. 



We should have gained very little if our theory did 

 no more than re-establish the results of classical me- 

 chanics on this rather fantastic basis. Its distinctive 

 merits begin to be apparent when we deal with pheno- 

 mena not covered by classical mechanics. We have 

 considered a stormy area of so small extent that its 

 position is as definite as that of a classical particle, but 

 we may also consider an area of wider extent. No 

 precise delimitation can be drawn between a large area 

 and a small area, so that we shall continue to associate 

 the idea of a particle with it; but whereas a small 

 concentrated storm fixes the position of the particle 



