Lec31 - MIT OpenCourseWare http/ocw.mit.edu 8.044 Statistical Physics I Spring 2008 For information about citing these materials or our Terms of

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Unformatted text preview: MIT OpenCourseWare http://ocw.mit.edu 8.044 Statistical Physics I Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms . 2 π / L x 2 π / L y k y k x D ( k ) = ( 2 π L x ) − 1 ( 2 π L y ) − 1 ( 2 π L z ) − 1 = V (2 π ) 3 wave vectors only! N = 2 × D ( k ) × 4 3 πk 3 F k F = 3 π 2 ( N/V ) 1 / 3 k z k x k y radius k F 8.044 L30B11 Fermions: Non-interacting, free, spin 1/2, T = 0 k z k x k y k F Fermi sea Fermi surface Fermi wave vector k F = 3 π 2 ( N/V ) 1 / 3 Fermi energy h 2 k 2 F = ¯ F / 2 m 8.044 L31B1 4 2 m 1 / 2 #( ) = 2 × D ( k ) × πk 3 ( ) k ( ) = h 2 3 ¯ 8 π V 2 m 3 / 2 3 / 2 = h 2 3 (2 π ) 3 ¯ V 2 m 3 / 2 1 / 2 D ( ) = h 2 2 π 2 ¯ D( ε ) h 2 k 2 ¯ F = 2 m F ∝ ( N/V ) 2 / 3 ε F ε 8.044 L31B2 D ( ) = a 1 / 2 F 2 N = D ( ) d = 3 a 3 / 2 0 F F 2 3 E = D ( ) d = 5 a 5 / 2 = 5 N F ∝ N ( N/V ) 2 / 3 0 F 8.044 L31B3 Consequences: Motion at T = 0 h h h ¯ p = ¯ k p F = ¯ k F v F = m k F Copper, one valence electron beyond a filled...
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This note was uploaded on 11/08/2011 for the course PHYSICS 8.004 taught by Professor Staff during the Spring '08 term at MIT.

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Lec31 - MIT OpenCourseWare http/ocw.mit.edu 8.044 Statistical Physics I Spring 2008 For information about citing these materials or our Terms of

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