Thanks for the reply, I realize it is hard for me to explain the question without writing up lots of the context that came before it. I will see if I can try to make more sense of it for myself and then if I can phrase it more clearly here, thank you anyway.
I need to work out an expression for the average of a Dirac delta-function
\delta(y-y_n)
over two normally distributed variables: z_m^{(n)}, v_m^{(n)}
So I take the Fourier integral representation of the delta function:
\delta(y-y_n)=\int \frac{d\omega}{2\pi} e^{i\omega(y-y_n)} =\int...
In that case I simply took the constant D to be 0, since it represents the amplitudes of waves coming in from the right side, and in that example I made the arbitrary assumption to consider waves being propagated from the left only. This made everything a lot easier, but here I don't think I can...
I am looking at a 1-d quantum system with a delta-potential barrier in the centre (at x = 0) and an infinitely high wall on one side of this barrier (at x = -a), while the system is open on the other side.
So the potential V is equal to:
V = κ\delta(x) at x = 0, κ being some constant and δ...