1. PHYS208 - spring 2010 - page 1 PHYS208 - Lecture Thursday 18. February 2010 Electrons in Metals Drude Lorenz Fermi Fermi Gas Comment:PLEASE READ THE DISCREPANCY STORY This text needs some more comments - to be added Includes: Slides from 2007 and 2008 The strange discrepancy between textbooks – Lorenz Number

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5. PHYS208 - spring 2010 - page 5 Solid State Physics [3C25] Tony Harker, Chiranijib Mitra and Andrew Horsfield (pages 117) Slides from 2007 and 2008 The strange discrepancy between textbooks

6. PHYS208 - spring 2010 - page 6 There are the following groups: 1. Kittel's book -> Wikipedia -> Hyperphysics -> Tony Harker et al -> some new textbooks factor 2 ( i.e. 2 pi 2 /9 ) larger than our derivation 2. Ashcroft&Mermin -> Burns -> Hemmer -> our derivation The difference is in the value of "average velocity". Wikipedia gives (2007) a nice review of the three velocities: Most probable, Average speed and Root Mean Square. The "Physical" is the root mean square, clearly, it relates to average energy. If we assume thet all particles have the velocity, this assumption must at least conserve the total energy! (It might be possible to argue for the average speed too.....) http://en.wikipedia.org/wiki/Maxwell-Boltzmann_distribution Slides from 2007 and 2008 The strange discrepancy between textbooks

7. PHYS208 - spring 2010 - page 7 The difference is in the value of "average velocity". Wikipedia gives (2007) a nice review of the three velocities: Most probable, Average speed and Root Mean Square. The "Physical" is the root mean square, clearly, it relates to average energy. If we assume thet all particles have the velocity, this assumption must at least conserve the total energy! (But it might be possible to argue for the average speed too.....) http://en.wikipedia.org/wiki/Maxwell-Boltzmann_distribution Slides from 2007 and 2008 The strange discrepancy between textbooks

8. PHYS208 - spring 2010 - page 8 Slides from 2007 and 2008 The strange discrepancy between textbooks

9. PHYS208 - spring 2010 - page 9 Slides from 2007 and 2008 The strange discrepancy between textbooks

10. PHYS208 - spring 2010 - page 10 Slides from 2007 and 2008 The strange discrepancy between textbooks

11. PHYS208 - spring 2010 - page 11 And Kittel - with the factor 2 result Slides from 2007 and 2008 The strange discrepancy between textbooks

12. PHYS208 - spring 2010 - page 12 And Kittel - with the factor 2 result ________________________________________________________________ Slides from 2007 and 2008 The strange discrepancy between textbooks

13. PHYS208 - spring 2010 - page 13 BACK TO 2010 Identity of particles -> phasefact=+1 or -1 + -> boson behaviour... they like to be crowded - -> psi a,a is identically zero Identity of particles -> Pauli exclusion «principle» Pauli exclusion «principle» -> Identity of particles ??

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19. PHYS208 - spring 2010 - page 19 SUMMARY Identity of particles -> phasefact=+1 or -1 + -> boson behaviour... they like to be crowded - -> psi a,a is identically zero therefore from Identity of particles follows Pauli exclusion «principle» Bose Einstein: Einstein invented that before quantum theory (photon behaviour - stimulated emission) Identity of particles -> Pauli exclusion «principle» Pauli exclusion «principle» -> Identity of particles ?? IN EACH (SPACE-based) STATE ONLY 2 PARTICLES (one in each spin state)

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21. PHYS208 - spring 2010 - page 21 The following is the two-parts of the scanned handwritten note on Fermi Gas The SUM to INTEGRAL transition is a major part of the derivation of the density in K space

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24. PHYS208 - spring 2010 - page 24 The lower part with today's comments

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