THE QUANTUM PHYSICS OF SOLIDS 



667 



atoms; b represents the sum of the wave functions and c the difference. 

 The process involved in getting these molecular wave functions is 

 mathematically similar to that of finding the normal modes for a sys- 

 tem of two similar coupled oscillators. In Fig. 9d we represent two 



lij a: 



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(b) 



(d) 



\ <--^1 ^~-^y T 



(e) 



(f) 



(9) 



INDUCTIVE 

 COUPLING 



Fig. 9 — A diatomic molecule and some mechanical and electrical analogues. 



(a) The potential energy of an electron for points on a line through 



the two nuclei. 



(b) and (c) Values of two wave functions for points on the same line. 



(d) Two coupled oscillators. 



(e) and (f) Their normal modes of vibration, 

 (g) Two coupled circuits. 



weakly coupled oscillators. The normal modes of vibration for the 

 coupled system are as indicated in Figs. 9e and 9/. These two modes 

 have different frequencies. Similarly if two electrical circuits are 

 placed so that there is some inductive coupling between them, we find 

 that each frequency is split into a pair. This inductive coupling is 

 similar to the overlapping of the wave functions; thus the coupling 

 between the circuits is large when the electromagnetic field of one 

 reaches over to the other. We may summarize the situation by saying 

 that before coupling each frequency occurred twice, once for each sys- 



