385lec18 - PHYS 385 Lecture 18 Degenerate matter Lecture 18...

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PHYS 385 Lecture 18 - Degenerate matter 18 - 1 ©2003 by David Boal, Simon Fraser University. All rights reserved; further copying or resale is strictly prohibited. Lecture 18 - Degenerate matter What's important : total energy of a fermi gas metals nuclei Text : Gasiorowicz Chap. 9, and other sources In the previous lecture, we examined the bound states of fermions in a 3D box, obtaining the spectrum of states and the maximum occupied state at zero temperature. Here, we perform one more calculation, namely the total binding energy, and two applications, metals and nuclei, before moving on to neutron stars in the next lecture. Degenerate matter - total energy Knowing both the density of states and the Fermi energy, the total energy of a degenerate Fermi gas is straightforward to calculate. We'll do the calculation specifically for spin 1/2 systems like electrons, protons or neutrons. The total number N of (spin 1/2) particles in a T = 0 Fermi gas is related to the maximum quantum number n max by N ( E E F ) = ( π /3) n max 3 . (spin 1/2) (1) The total energy E TOT is obtained by integrating the energy of each state E n = n 2 π 2 h 2 / mL 2 (spin 1/2) over the allowed states: E TOT = (1/8) o nmax E n d
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This note was uploaded on 09/07/2009 for the course PHYS 385 taught by Professor Davidboal during the Spring '09 term at Simon Fraser.

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385lec18 - PHYS 385 Lecture 18 Degenerate matter Lecture 18...

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