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BELL SYSTEM TECHNICAL JOURNAL 



tern; after coupling two frequencies are present and the corresponding 

 modes of vibration belong not to the individual systems but instead 

 to the pair of systems. For the case of atoms each quantum state 

 occurs twice, once for each atom, before the atoms interact; after inter- 

 action there are still two quantum states but now they have different 

 energies and are shared by both atoms. 



As the atoms are brought closer together the energies separate more 

 and more. The behavior is indicated qualitatively in Fig. 10. The 



INTERNUCLEAR DISTANCE (OR STRENGTH OF COUPLING) 



Fig. 10 — Energy levels of a diatomic molecule versus internuclear distance. 



L levels (25 and 2p) split at larger distances than the K levels because 

 their wave functions extend farther from the nucleus (see Figs. 7 and 8) 

 and overlap at greater distances. The details of the splitting are 

 somewhat complicated and only the start is shown here. For the 

 mechanical analogues shown in Fig. 8, the coupling raises one fre- 

 quency and leaves the other unaltered. On the other hand, the 

 quantum mechanical interaction results, at large distances, in equal 

 displacement up and down for the energy levels. 



We can use Fig. 10 to describe the formation of a molecule of 

 hydrogen, H2. We start initially with the single electron of each atom 



