Hi, I am in the process of learning QM. I am looking at this problem regarding to a finite square potential well. I have derived psi(x) and the k's for the 3 domains, psi1(x) = Ae^kx => k = sqrt(2m(V-E)/h^2) psi2(x) = Ce^jkx + De^-jkx => k=sqrt(2mE)/h psi3(x) = He^-kx => same k as in domain 1 and then what I did was to take the boundry conditions and substitue into the equations and make a system of 4 equations with so that I can solve the unknowns. What I don't understand is the way I've been told to do this from the above. I've been told to calculate the determinant of the system of the 4 equations, and by scanning E. When the determinant goes to 0, I will get the energy level for E. Any one can explain to me why this will give the answer? And also, it seems like I will need to get the answer by ploting the determinant from its imaginary component. Why? And when I have the 3 different energy levels that satisfy the conditions, how do I find the unknowns? Thanks for any help.