07hw - Solutions to problem set 7 (141A Sp07) 1 1. (ISSP...

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Solutions to problem set 7 (141A Sp07) 1 1. (ISSP 6.9) Consider the steady state equations for the velocity, equation (52) page 153 of ISSP. Multiply- ing across by n ( - e ), gives (using ~  = n ( - e ) ~ v etc), j x = σ 0 E x - ω c τ j y j y = σ 0 E y + ω c τ j x j z = σ 0 E z where σ 0 = ne 2 τ/ m . Rewriting: 1 ω c τ 0 - ω c τ 1 0 0 0 1 j x j y j z = σ 0 E x E y E z Inverting: j x j y j z = σ 0 1 + ( ω c τ ) 2 1 - ω c τ 0 ω c τ 1 0 0 0 1 E x E y E z In a high magnetic field, σ yx = σ 0 ω c τ 1 + ( ω c τ ) 2 ' σ 0 ω c τ = ne 2 τ m mc eB τ = nec B 2. (a) The Schr¨odinger equation gives - ~ 2 2 m 2 ψ = E ( ~ n
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07hw - Solutions to problem set 7 (141A Sp07) 1 1. (ISSP...

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