﻿Binding of Electrons by Atoms. 201 



The variation of p x between + v/2mW at infinity is the 

 source of trouble, and it takes place while - =0. 



p, = - VJmW 



e = 277—77 



Epstein takes twice the integral from </> = to <£=7r, but 

 according to the substitution formula, r is negative when <£ 

 goes frpm 77 to 77-, and negative values of r are clearly not 

 permissible. A suitable integration for the infinite region 

 cannot in fact be effected, and any supposition of a suitable 

 variable in place of <£>, for the change of p 1 at 00 from 

 V2mW to — \Z2mW, would be entirely arbitrary, — but as 

 it could not lead to a finite phase-integral, we pursue the 

 matter no further. 



These considerations, nevertheless, have considerable force 

 when, thrown back as we now are upon the necessity, if the 

 quantum theory is applicable, of using p l — (pi) mJ we attempt 

 to quantize this. 



We have, when # = 77 



k>i).= ^2mW 

 = -* sin 77, 



where g= \/m 2 i>V + 2m W/3 2 as before. 

 And when </> = 27r — 77, 



• (#)•= £ sin (27T-77) = - I sin 77. 



From </> = to $=77, 



Pi - (Pi)oo = I ( sin 9 - sin f) • 

 From <f) = 27r — n to </> = 27r, 



Pi - (Pi)* = + I ( sin * + sin ^ 

 and from (p = r) to $ = 27r — ?7, 



