406 BELL SYSTEM TECHNICAL JOURNAL 



distance V{nh)l. One can, in fact, easily verify that this construction gives a 

 solution of (4), by writing (4) in the form 



/dnh\ 

 \cVji 



'II,, (^_!!h\ 



whence it is obvious that the function «./.(.t, /) defined implicitly by 



x(n,, , t) = x{n, , 0) + V(nH)t 



satisfies (4) for any form of the arbitrary function x(nh , 0), and that, con- 

 versely, any solution of (4) must be of this form. 



Assuming, as in the preceding, that all currents flow from left to right, 

 the boundary conditions a,t t = 0^ are : 



fih = Oiorx < and x- > (8) 



or, equivalently, 



E = Ea= ia/o-o for x <0] . 



E = E,= {ja^-je)/<T, for X > o) 

 The boundary conditions at a; = are, for ; > 0, 



wa = or, equivalently, E = E^iox x = Qr (10) 



and 



nh = iihi or, equivalently, E = Ei , for x = 0+ (11) 



where £i and nia are given by the requirement of continuity of electronic 

 current, i.e., 



EaUolJ-e = -El(«0 + «/a)Me 



whence, using the relation (3) between Ei and rihi and expressing £„ as 



ja/noeiJLe 



fihi = 



no (12) 



or, alternatively, 



£i = £o I 1 - 



iaMfc _ J 



r_Gf^±MO ie 1 (13) 



L Mft (7a + Je)J 



According to (12), Uhi is small when j<, is small; and, by (13), £i is only 

 slightly below Eo for this case. As^e mcreases, riu increases and £i decreases, 



