Which Equation Should Be Used for QC 8.7 in Zwiebach?

[ehrenfest]

Homework Statement

http://books.google.com/books?id=Xm...ts=cV3Uhs4Tnr&sig=C_bLwW8j_Nyc4sM0fJWooLkGLDY
I am trying to do QC 8.7. If I use the equation given on page 127, l = 2/pi E/T0, I do not think that produces right answer. Is there another equation I should use
?

Homework Equations

The Attempt at a Solution

 

[Jimmy Snyder]

Is there another equation I should use?

You should use equations (3.88) on page 54 but replace the equation for G with the equation for $\alpha'$. Then follow the technique on that page.

 

[ehrenfest]

Sorry, can you explain what you mean replace the equation for G with the equation for alpha' (8.63 I assume)? G and J/hbar do not even have the same units.

 

[Jimmy Snyder]

Sorry, can you explain what you mean replace the equation for G with the equation for alpha' (8.63 I assume)? G and J/hbar do not even have the same units.

There are three equations labeled (3.88). Replace all of the P subscripts with S. Toss out the equation that defines G and use equation (8.63) in its place. Express $\sqrt{\alpha'}$ in terms of ${l}_S, {m}_S,$ and ${t}_S$.

 

[ehrenfest]

OK. I see why that works. My only concern is how do you know that you can replace the p subscripts with s subscripts. Those relations are only true in the Planckian system of units, right?