- #1

holden

- 30

- 0

"A particle of mass m and energy E > 0 approaches a potential drop -V0 from the left. What is the probability that it will be reflected back if E = V0/3? The potential energy is V(x) = 0 for x<0 and V(x) = -V0 for x>=0."

So what we're looking for is R, the reflectivity constant. My book tells me a formula for 1/T for this case (E > 0, V < E), but that's for a rectangular well and includes the width of the well in the formula.. and this one is infinite.

What I've tried to do so far is using [tex]\frac{d^2\psi}{dx^2} + \frac{2mE}{\hbar^2}\psi = 0[/tex] for the Schrodinger's equation to the left of the well. I'm not really sure why I'm using this other than it's in my notes (cause V(x) is zero?). So from this I'm getting [tex]\psi(x) = Ae^{\frac{i\sqrt{2mE}x}{\hbar}} + Be^{\frac{-i\sqrt{2mE}x}{\hbar}}[/tex].

I know R = abs(B/A)^2.. but I'm not sure what to do next. I think apply the boundary conditions..? I'm really lost on how to do that.. I think I'm missing something fundamental here.

Thanks in advance for the help!