THE QUANTUM PHYSICS OF SOLIDS 



665 



wave patterns are determined not only by the values of mass per unit 

 area, a, and tension, T, of the membrane but also by the "boundary 

 condition" that it be clamped on its rectangular edge; at this edge the 

 vertical displacement <p must vanish. The corresponding boundary 

 condition for the atom is that the wave function \l/ vanish at all points 

 infinitelv far from the nucleus. 



Fig. 8 — The electron charge densities for four wave functions. Cross-sections 

 are given for the \s and 25 wave functions and perspective views for the 2p. Is rep- 

 resents a ball of charge; 2^, a ball surrounded by a shell; 2p m = 0, a dumbbell-like 

 distribution; 2p m = ± 1, a doughnut-like distribution seen edgewise. ' 



The quantity [t^I^ has a direct physical interpretation: its value 

 at any point in space gives the probability of finding the electron at 

 that point. If it were possible to take a photograph of the electron's 

 motion with a time exposure so long that a true average of its positions 

 would be obtained, this photograph would represent \^\-. In Fig. 8 



