5/15/11

Question about assignment 4

Can anyone find out how to get the factor of 2 in q2 for m*/m = UG/2E0(G/2)? becuase like the tutorial again I got m*/m = 2UG/E0(G). In the tutorial we also got E0(G) instead of E0(G/2), and I got the same result as tutorial again. I think maybe we should follow some other way. can anyone help me with it?
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3 comments:

  1. 助守和May 15, 2011 at 11:07 PM

    It's just a matter of rearranging
    1/(E0(G)) = 1/((hbar^2 G^2)/(2m)) = 2m/(hbar^2 G^2) Right?
    Therefore, 2UG/E0(G) = 2UG(2m)/(hbar^2 G^2)
    Now if you multiply this by 2/2, you get
    (UG 2m*4)/(2*hbar^2 G^2) = (UG/2)*1/(hbar^2 G^2)/(2m*4)
    G^2/4 = (G/2)^2,
    therfore (hbar^2 G^2)/(2m*4)= E0(G/2)
    giving UG/(2E0(G/2))

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  2. negarMay 16, 2011 at 11:11 AM

    if I follow your way I got an extra m and my result would be m(UG)/2*E0(G/2), because from the Paul's way we reach to 2m(UG)/E0(G), and now we have 1/E0(G) = 2m/hbar^2*G^2 and if we multiply the both sides by 2m(UG) to reach to 2m(UG)/E0(G), (Paul's answer) we got extar factor of m in our answer and the result would be m(UG)/2E0(G/2)

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  3. negarMay 16, 2011 at 11:41 AM

    I got it thanks to Josh.
    I forgot that we want to find m*/m. my answer was m* = m(UG)/2E0(G/2), so m*/m = (UG)/2E0(G/2)

    Thanks Josh.

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