% Annihilation, creation and number operators (Sec. III.A)
%   a|n> = sqrt(n)|n-1>,   a'|n> = sqrt(n+1)|n+1>,   N = a'a,  N|n> = n|n>
% The creation operator is the adjoint of the annihilation operator.

clear;                      % Clear memory
clc;                        % Clear the command window/screen
d = 6;                      % dimension of the operator
A = diag(sqrt(1:d-1), 1)    % Annihilation operator (superdiagonal)
Ad = A'                     % Creation operator (adjoint of A)
N = Ad*A                    % Number operator (diagonal: 0,1,2,...)