% Coherent state (Sec. II.C)
%   |alpha> = exp(-|alpha|^2/2) * sum_n alpha^n/sqrt(n!) |n>
% The infinite sum is truncated at d-1; check that the norm stays ~1.

clear;          % Clear memory
clc;            % Clear the command window/screen
d = 10;         % dimension of the field
I = eye(d);
alpha = 0.6;    % amplitude of the coherent state
Coh = 0;        % initialization
for x = 0:d-1
  Coh = Coh + exp(-norm(alpha)^2/2)*alpha^x/sqrt(prod(1:x))*I(:,x+1);
end
Coh             % display the coherent state
N_c = norm(Coh) % check norm (should be very close to 1)