"Problem 15.1.2" ahat(f) = sqrt(1/2) (f xi + d(f,xi)) ahatdag(f) = sqrt(1/2) (f xi - d(f,xi)) ket0 = pi^(-1/4) exp(-xi^2 / 2) -- see equation (15.33) ket(n) = test(n < 0, 0, n == 0, ket0, sqrt(1/n) ahatdag(ket(n - 1))) A(n) = ahatdag(ahat(ahatdag(ket(n)))) B(n) = (n + 1) ahatdag(ket(n)) -- check for n = 0 to 10 for(n,0,10,check(A(n) == B(n))) "ok" Run