CONTEMPORARY ADVANCES IN PHYSICS 655 



surrounding nuclei; diatomic molecules, as paired nuclei surrounded 

 by their jointly shared electron-family, capable of revolving like a 

 dumbbell around their centre of mass and of vibrating like the two 

 ends of a spring along their line of centres. These pictures persist in 

 wave-mechanics; but the permitted vibration-amplitudes, the per- 

 mitted rotation-speeds, and the permitted electron-orbits adduced to 

 symbolize the Stationary States languish for the moment in the same 

 discredit as the permitted elliptic orbits of the hydrogen atom. 



Meanwhile, the humiliation of the electron-orbits accentuates the 

 grave defect of the original atom-model of Bohr. That model offered 

 nothing to interpret the fact that when an atom passes between two 

 Stationary States of energy-values (let me say) Ei and Ej, it emits (or 

 absorbs) radiation of the precise frequency {Ei — Ejj/h, the quotient 

 of the energy-difference by the notorious constant of Planck. Neither 

 in the initial State nor in the final State are the constituent parts of 

 the atom-model vibrating with this frequency (except in occasional 

 untypical cases). The frequencies of the waves streaming out from 

 the atom do not agree with the frequencies of the motions assumed 

 to exist inside the atom — a very uncomfortable idea, altogether dis- 

 cordant with all our experience of sound and electrical circuits. 



If it should be found possible to incorporate into the atom-model 

 something vibratory, having for its vibration-frequency the quotient 

 of the energy-value of the then-existing Stationary State by Planck's 

 constant: then in the foregoing case this "something" would be 

 vibrating initially with frequency Ei/h and finally with frequency 

 Ej/h, and the frequency of the emitted radiation would be the hetero- 

 dyne or beat-frequency of these two. This is an agreeable idea; and 

 wave-mechanics offers it. If then it should be found possible to 

 arrive at the energy-values of the Stationary States by imposing 

 conditions upon this vibrating entity instead of the electron-orbits, 

 we should achieve as much as the electron-orbits enable us to achieve, 

 and have the foregoing advantage also, and perhaps others as well. 

 This is what wave-mechanics promises. 



To this introduction I wish to join two warnings before plunging 

 into the exposition. In the first place, wave-mechanics has several 

 aspects, and may be approached from several directions ; the one which 

 I have chosen for this article is not the one which de Broglie elected 

 nor the one which Schroedinger prefers.^ In the second place, wave- 



^ I suspect that the method of exposition which I shall follow is the one which 

 Schroedinger meant when he wrote "I had originally the intention of establishing 

 the new formulation of the quantum-conditions in this more visualizable (anschaulich) 

 way, but preferred a neutral mathematical form, because it makes the essence 

 clearer." Schroedinger himself stresses the formal likeness between ordinary me- 



