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## Main Question or Discussion Point

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.

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.

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