Quick Potential Barrier tunnelling question

[Novocaine]

I am dealing with the classic problem of a potential barrier of finite width, with a particle tunneling through, in the case of E < V.

I am to calculate the transmission/reflection coefficients, and we first start off with the wavefunctions for the three regions.

Before the barrier, we have Aexp(ikx) + Bexp(-ikx)

In the barrier, we have Cexp(k1x) + Dexp(-k1x)

After the barrier, we have Fexp(kx).

My only question about this is where the i term comes from. It is probably a very simple answer but I want to know exactly its reason before I go on past this point. In the case of E > V, the i term appears in all the exponentials. Thank you.

 

[malawi_glenn]

It comes from the soloution to the second order ordninary differential equation.

Try to see how these wave functions comes, when solving the shrodinger equation for the different regions for your potentia:

"Before the barrier, we have Aexp(ikx) + Bexp(-ikx)

In the barrier, we have Cexp(k1x) + Dexp(-k1x)

After the barrier, we have Fexp(kx)."