Solution4JT+TW

# Solution4JT+TW - Solutions of Problem set 4 PHYS 361(Solid...

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Unformatted text preview: Solutions of Problem set # 4 PHYS 361 (Solid State Physics), Autumn 2009 1. Surface plasmon vs thin-film plasmon (a) Think about the new position of e- : x = x + u ( x ), the total number of electrons n s · dx · D in a strip of | dx × D | is does not change after they move to a new area | dx × D | : n e ( x ) · dx · D , where D is some length in y direction. Thus n e ( x ) = n s dx dx = n s 1+ qu cos( qx ) ≈ n s (1- qu cos( qx )). However there are compensating uniform background charges with density n s , therefore the total charge density is the difference between the above two: n s ( x ) = e · n s- e · n e ( x ) = eqn s u cos( qx ). There are several other ways doing this. (b) The potential of line segment dx of charge density n s ( x ) at a point with distance r to the axis of the line is dφ ( r ) = λ 2 πε ln r r , where r is some reference point of the potential and λ = n s ( x ) · dx . Therefore φ ( x ) = R dx n s ( x ) 2 πε ln r x- x = en s u 2 ε cos( qx ) (c) the potential energy density is...
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Solution4JT+TW - Solutions of Problem set 4 PHYS 361(Solid...

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