Situations of ground state dominance

Note that c is proportional to the square of ifi this is because two chain portions converge at point s, each carrying a factor i]r. The normalization in eq. (IX. 18) is easily checked since /c(s) = N for a one-chiun problem. 

The validity of the truncation is, of course, limited. One has to cheek that the intervals are large enough to make the ground state 

Exercise I One ideal chw confined between two strongly repulsive walls (separation D R ). Compute 1) the reduction of entropy, and 2) the concentration profile (E. Cassasa).  

Answer If we put the walls at jr = 0 and x = , the eigenfimctions Uit must vanish at both walls. Inside the interval they satisfy c = (-o /6) ITie ground state is simply 

The main factor in the statistical weight is exp - N), giving an entropy reduction 

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