709 



Substituting the expression U) for ^ in equation (3), «e ha7« 

 or, i^>on substituting for $ the expression (Aa), 







[j^A-A^'^^^i^l " 



We shall assume a Hankel transform -ji (yKt ^ > ^ ) for toe oyllndrlcally symmetric 

 solution # ( A > Z > t" ) , namely. 



nhere 





Ub 



•ad X(*A) is the Bessel function of zero order. Substituting this expression for $ 



s 



in equations (1') and (2') and commuting operators, we obtain, respectively. 



Applying the inverse transformation and recalling that iteration of this operator is 

 equivalent to multiplication by unity, we find 



% - n - 



at 

 'ii 



- O 

 a z /z = 



These conditions are satisfied by 



^(A,zt) - kMc^-^' 



