function H = constructHamiltonian(x);

% CONSTRUCTHAMILTONIAN function to prepare an (N-1)*(N-1) matrix 
%    representing the sum of kinetic and potential energy operators.

global hbar eV m;

N      = length(x) - 1;
deltaX = (max(x) - min(x))/N;

off     = ones(N-2,1);                 % same as secDriv.m
secDiff = -2*eye(N-1) + diag(off,1) + diag(off,-1);
A       = secDiff/(deltaX^2);

KE = -hbar^2/(2*m*eV) * A;            % build the KE matrix

PE = zeros(N-1);                       % build the PE matrix 
for j=1:(N-1)
    PE(j,j) = potential(x(j+1));
end;

H = KE + PE;
return;