666 BELL SYSTEM TECHNICAL JOURNAL 



we show the predicted patterns as obtained by H. E. White,® who 

 photographed a model representing the wave functions. We see that 

 for the 25 wave function the electron is much farther from the nucleus 

 on the average than for the I5; this accounts for higher energy of the 

 25 state. For a hydrogen atom the 25 and 2p actually have the same 

 energy. For other elements the 25 lies lower as shown in Fig. 2; this 

 is because an electron in the 25 state penetrates the K shell and feels 

 the full charge of the nucleus whereas an electron in the 2p state stays 

 outside of the K shell and is thus shielded from the nucleus by the two 

 electrons of the K shell. 



For purposes of illustration we have considered the rectangular 

 drumhead as a mechanical analogue for the wave equation. Other 

 analogues are represented by sound waves in rooms and in organ pipes 

 and by standing electromagnetic waves in wave guides, tuned cavities, 

 and rhumbatron oscillators. We shall use two simple analogues in our 

 later discussion. One is the mechanical vibrator represented in Fig. Id 

 which we consider to be restricted to vertical motion. It is a system 

 with a single frequency — like an imaginary atom with only one possible 

 state — and its one normal mode of vibration is a simple harmonic 

 motion up and down equally far above and below its equilibrium posi- 

 tion as indicated in Fig. 7e. The other is an electrical analogue, Fig. 7/, 

 consisting of a section of transmission line terminated at each end by a 

 high inductance. This system has a series of normal modes of vibra- 

 tion and a related series of allowed frequencies. The allowed fre- 

 quencies correspond to the energy levels of the atom. 



Electrons in Molecules 

 We shall next consider what happens when two atoms are brought 

 so close together that their quantum states "interact." Two similar 

 atoms widely separated have each a distinct set of quantum states and 

 wave functions and the scheme of energy levels for the two atoms is 

 obtained by duplicating the energy level scheme of Fig. 2. However, 

 if the atoms move so near together that the wave functions for the 

 corresponding quantum states of the two atoms overlap, there is an 

 alteration in the energy levels. Figure 9 is intended to illustrate this 

 process. Figure 9a shows the potential energy of an electron for 

 points on a line passing through the centers of the two nuclei, and Figs. 

 9b and 9c show for points on the same line the values of the correct 

 wave functions in this field. These wave functions are obtained, 

 approximately, by using the \s wave function for the two separate 



^Physical Review, 37, 1416 (1931). I am indebted to Professor White for the 

 photographs used for these illustrations. 



