CONTEMPORARY ADVANCES IN PHYSICS, XXVIII 599 



the particle for awhile, and to conceive a train of waves advancing 

 from infinity towards the nucleus. The phase-speed and the fre- 

 quency of this wave-train are prescribed by definite rules making them 

 dependent upon E, and the train is governed by a prescribed wave- 

 equation in which figures the function Vir) of Fig. 12. On solving 

 this equation in the prescribed fashion we find that it requires the wave- 

 train to continue (though reduced in amplitude) past the top of the 

 hill if K is greater than neVm. This is partially satisfactory, for the 

 particle when it is reintroduced is to be associated with the waves, 

 and everything would be spoiled if the particle could go where the 

 waves cannot. But also, the equation requires the wave-train to 

 continue past the top of the hill when K is less than neVm- True, it 

 does not wholly pass; there is a reflected as well as a transmitted beam, 

 and the ratio of reflected to incident amplitude goes very rapidly up 

 towards unity and the ratio of transmitted to incident amplitude goes 

 very rapidly down toward zero as K drops downward from the value 

 neVm- All the same there is this wave-train beyond the hill with an 

 amplitude greater than zero; and the association of particles with 

 waves is apparently spoiled, for the waves can go where the particle 

 cannot. 



At this point, however, it is the rule of theoretical physicists to 

 give the precedence to the waves, and declare that where the waves go 

 there the particle must go also, whether it can (by classical mechanics) 

 or cannot. Since some of the waves are beyond the hill, the particle 

 also must be able to traverse the hill, even though its kinetic energy is 

 insufificient for it to climb to the top. But since the waves beyond the 

 hill have a smaller amplitude than those coming up from infinity, it 

 is not certain that the particle will pass through, but merely possible. 

 The chance or probability of its passing through is determined chiefly 

 (not fully) by the ratio of the squared-amplitudes of the waves on the 

 two sides of the hill, and this is what must be computed by quantum- 

 mechanics. How the particle gets over or through the hill — -where 

 and what it is and how it is moving while it is getting through — these 

 are questions which the theorist usually declares to be unanswerable 

 in principle, and having so declared, he does not attempt to visualize 

 this part of the process. 



Into Fig. 12 the diagonal lines have been introduced in a crude 

 attempt to make graphic as much as possible of the theory. The 

 length of the sloping line drawn from any point P of the curve is 

 meant as a sort of inverse suggestion of the chance which a particle 

 of charge -f ne has of entering the nucleus if its energy E is equal to 

 ne times the ordinate of P: the longer the line, the less the chance of 



