I have been trying to find the eigenenergies the Hamiltonian using the eig() function
% constants and parametershbar = 6.58211*10^-4;w1 = 2000/hbar;w2 = 2001/hbar;syms wph;g = 120;pump = 10;% the hamiltonianh = [w1-wph pump 0;pump w1-wph g;0 g w2];
This gives complex valued eigenenergies in terms of the parameter wph. This was expected because Matlab might be using an algorithm sue to which this happens. I also expected that when I plot these values against wph, they should be real but instead they come out to be complex valued with a fairly big imaginary part (code attached).
Can anyone explain why this is happening? The hamiltonian is hermitian and thus should have real eigenenergies which is not happening.