quiz2_soln
2
2 2 2 ) ( . 2 . ) 2 ( int 2 , 1 ) exp( ) ( ) ( . . 2 ), exp( 1 2 : 1 1 Δ Δ − = = ⇒ = ⇒ = + = = = ll d L k i k i k l h spin including states allowed contains It space k in L element length consider egers n where L n k ikL x L x c b periodic use m k E ikx L m p H system electron free D Consider prob h π π ψ ψ ψ 2 / 1 2 2 / 1 2 2 / 1 2 2 2 1 ) ( 2 2 1 2 2 ) ( , , 2 2 * ) ( . int . , − − − = = ⇒ = = ∂ ∑ ∂ = + = = = − = Σ = Δ − Δ ⇒ E m E g length unit per states of density E E m L E E m L E E E E E ene and E ene states allowed of No mE L space k in length L E E energy upto states allowed of No E energy with po energy const consider states allowed k contains space k in k length h h h h π δ π δ π δ δ π π π 3 2 3 2 6 0 3 0 3 , , 0 0 , 0 0 : , 0 . ' 1 1 , 1 : Reminder ) ( 2 1 ) ( 2 1 ) ( ) 2 ( ) ( ) ( 2 : ) ( , 2 1 2 ) 2 2 2 / 3 3 2 2 2 2 2 3 3 2 / 3 3 2 / 3 3 3 2 / 3 3 2 / 3 2 2 2 = = = = = + + = − = + + + + + + + = + = + = ⇒ + = = + + = + + + + + + + + + + + + + + + + + ω λ ω λ ω λ ω λ ω λ ω ω ω λ ω ω ω λ ω h h h h h h h h h h h a W thus a a a note W n need op this by state ground to connected are states which see s Let n n n a n n n a a aa aa a a a aa a a a a a a a a a a m m W a a m X use X m W W X m m p H prob ... ] 3 3 2 1 1 2 3 [ 0 ... 3 2 3 3 1 1 2 3 1 0 ... 0 0 8 11 ] 3 4 / 3 8 / 9 [ ) ( ) 2 1 ( : , 0 3 0 1 ... 0 0 0 . 0 2 3 2 ) 1 2 ( 0 1 0 1 2 / 3 2 / 3 0 0 2 2 0 3 0 2 1 0 2 0 0 2 0 2 / 3 2 / 3 2 + + − = + − − = + − + = = + − = Δ ⇒ + = − + − = + − + = Δ = + = + = ∑ ∑ ≠ ≠ + + + λ ω λ ω ω λ ω ψ ω λ ω ω ω λ ω ω λ ω λ h h h h h h h h h h h n E E W n E n E use E E W E E W E E W n W E are elements matrix other all aa a aa W n n n n n
description
ds
Transcript of quiz2_soln
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