﻿Binding of Electrons by .Atoms. 195 



writers on tlie quantum theory of spectra, that the energy W 

 is always completely determinate when all the momenta are 

 quantized. This can be disproved not only for fictitious laws 

 of force in an atom, but for laws which must actually occur 

 in systems with an existence, if only a temporary one. 



Consider, for example, a simple doublet and an electron 

 in orbital motion about it. Regarding the doublet as 

 stationary, and of moment M, its external potential is 



M cos 

 ~ r* 



when it is situated at the origin, with its axis along the axis 

 of z, using spherical polar coordinates. The equation of 

 energy for an electron moving in its presence is 



im {r 2 + r 2 fl 2 + r 2 sin 8 6 j> 2 } 4- M * C 8 ° S ° = - W. 



The momenta are, in the usual notation, 



BT . BT %d 



Pi = 57. = mr > Pi = ^ = mr .°> 



Jh — ;— r- — mv 2 sin 2 0$, 

 09 



so that 



Me cos 6 



I r r L siir V J r l 



= -w. 



Xow <f> is a speed coordinate as usual, so that 



p z == const. = n-Jifeir 



when subjected to the quantum relation: n x being an integer. 

 For the Jacobi solution, we must also take, in separating 

 variables, 



P2 2 + ~P\a + 2mMe cos e =/3 

 £ suv 6 ^ 



where /3 is constant, and 



>{pi 2 +^} = -w. 



Thus 



-2mW-J. 



02 



