THE QUANTUM PHYSICS OF SOLIDS 



655 



levels represented on Fig. 2 apply to unoccupied and occupied states 

 as well. 



I have already mentioned that four quantum numbers are required 

 to specify each quantum state. These are indicated by the letters 



1=3 



1=2 



1=1 1=0 1=0 1=1 



1=2 



1 = 3 



4f 



J— I 4d 



III I.I 4p 



3d ^^^ 



I I 1- 



4f 



4C| I I I I I 1 L 



4p I I I I I I 



^-^^ 3d 

 45 1 I I I |_j 



3P 



J l__l 



2p 



J I I 



3P 



I I I I 



2P 



1_J L 



-2-1 I 2 = m 



-spiN^ nns=-^ 



+ SPIN, ms= + 2 



Fig. 2 — Quantum states for electrons in atoms. 



w, /, m, and fUs- Roughly speaking, the "principal quantum number 

 w" fixes the "energy level" of the state; however, there is some de- 

 pendence upon the "angular momentum quantum number /." The 

 dependence of energy upon the third quantum number, "the magnetic 

 quantum number m," is slight and will be neglected in this paper. 

 We shall consider the energy to be specified by giving n and /. A 

 notation borrowed from spectroscopy is applied to this pair of quantum 

 numbers and one uses the apparently quite fortuitous choice of 

 letters s, p, d, f, g, h, etc., to stand for / = 0, 1, 2, 3, 4, 5, etc., and a 

 state with n = 3 and / = 2 is known as a "3d state" and an electron 

 occupying such a state is called a "3d electron." The quantum laws 

 permit the following values for n, I, and m: 



n takes on all positive integral values. (All states with n greater 

 than four have been omitted from the figure; they lie between 

 the highest states shown and zero energy.) 



