78 AVERAGE VALUES IN A CANONICAL 



or since by (218) 



-e) = e(e-e) - A <- 



In precisely the same way we may obtain for the potential 

 energy 



(6 3 -i 3 )^ = @ 2 ^(e 3 - e q ^ + h(e q - e q )^ 2 g. (232) 

 By successive applications of (231) we obtain 



(e - i) 2 = 

 (e-e) 8 = 



(e - e) 6 = J> 5 e + 15DeD*e + 10(D 2 ) 2 + 15(Z)e) 8 etc. 



where D represents the operator ' 2 d/d. Similar expres- 

 sions relating to the potential energy may be derived from 

 (232). 



For the kinetic energy we may write similar equations in 

 which the averages may be taken either for a single configura- 

 tion or for the whole ensemble. But since 



dp _ n 



d~2 



the general formula reduces to 



(e p - e p ) = 2 A (p - e p ) + n h& (e p - ~e p )^ (233) 

 or 



(234) 



