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author | bnewbold <bnewbold@eta.mit.edu> | 2009-03-19 14:32:23 -0400 |
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committer | bnewbold <bnewbold@eta.mit.edu> | 2009-03-19 14:32:23 -0400 |

commit | 08a1d77053372b310055ddde8621c6b8a206ef50 (patch) | |

tree | 9e145f93b47be0c42def3674df1adcb029c76c44 /physics/quantum | |

parent | 8d74e58abcb07a030201c65f3522e973903ad6ef (diff) | |

download | knowledge-08a1d77053372b310055ddde8621c6b8a206ef50.tar.gz knowledge-08a1d77053372b310055ddde8621c6b8a206ef50.zip |

corrections to fermi, TODO check second to last line

Diffstat (limited to 'physics/quantum')

-rw-r--r-- | physics/quantum/fermigas | 11 |

1 files changed, 5 insertions, 6 deletions

diff --git a/physics/quantum/fermigas b/physics/quantum/fermigas index b91c67c..0114b43 100644 --- a/physics/quantum/fermigas +++ b/physics/quantum/fermigas @@ -39,14 +39,13 @@ correction can be important. There will then be a second correction due to removing the states along the individual axes twice (once for each side-surface), u.s.w. -The surface of this shell is called the Fermi surface -and represents the most excited states in the gas. The radius can be derived -by calculating the total volume enclosed: each block has volume -:m:`$\frac{\pi^3}{l_x l_y l_z}=\frac{pi^3}{V}$` and there are N/2 blocks occupied by N -fermions, so: +The surface of this shell is called the Fermi surface and represents the most +excited states in the gas. The radius can be derived by calculating the total +volume enclosed: each block has volume :m:`$\frac{\pi^3}{l_x l_y +l_z}=\frac{\pi^3}{V}$` and there are N/2 blocks occupied by N fermions, so: :m:`$$\frac{1}{8}(\frac{4\pi}{3} |k_{F}|^{3})&=&\frac{Nq}{2}(\frac{\pi^{3}}{V})\\|k_{F}|&=&\sqrt{\frac{3Nq\pi^2}{V}}^3=\sqrt{3\pi^2\rho}^3$$` :m:`$\rho$` is the "free fermion density". The corresponding energy is: -:m:`$$E_{F}=\frac{\hbar^{2}}{2m}|k_{F}|^{2}=\frac{\hbar^{2}}{2m}\sqrt{3\rho \pi}^3$$` +:m:`$$E_{F}=\frac{\hbar^{2}}{2m}|k_{F}|^{2}=\frac{\hbar^{2}}{2m}(3\rho \pi)^{2/3}$$` |