- #1

roam

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## Homework Statement

I need help with part (iii) and (ii) of the follwoing problem:

http://img228.imageshack.us/img228/516/79620850.jpg [Broken]

## Homework Equations

From my notes transmission coefficient for E<U is:

[tex]T(E)= \left[ 1+\frac{1}{4} \left( \frac{U^2}{E(U-E)} \right) sinh^2 (\alpha L) \right]^{-1}[/tex]

And for E>U it is:

[tex]T(E)= \left[ 1+\frac{1}{4} \left( \frac{U^2}{E(E-U)} \right) sin^2 (k' L) \right]^{-1}[/tex]

Where [tex]k'=\frac{\sqrt{2m(E-U)}}{\hbar}[/tex] and [tex]\alpha =\frac{\sqrt{2m(U-E)}}{\hbar}[/tex].

## The Attempt at a Solution

So for part (ii). I used the first equation and got a value of 4.59x10

^{-4}. This doesn't seem like a correct number for the number of neutrons. So do I have to multiply this with the total number of neutrons?

For (iii) I am confused and I don't know which equation to use. We know the equation when E<U and when E>U, but what exactly is the equation for when E=U?

I don't quite understand the hint, does this mean we need the following equation:

[tex]T(E)= \left[ 1+\frac{1}{4} \left( \frac{U^2}{E(U-E)} \right) \alpha^2 L^2 \right]^{-1}[/tex]

Is that right?

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