2009.04.22-ECE659-L38-notes

# 2009.04.22-ECE659-L38-notes - following linear combinations...

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ECE 659 Quantum Transport: Atom to Transistor Lecture 38: Singlet/Triplet States Supriyo Datta Spring 2009 Notes prepared by Samiran Ganguly

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H U + s Σ 2 Σ 1 Σ 1 μ 2 1 γ 2 0 1 One electron picture Multi-electron picture I 2 2 q × N electrons -> 2 N states in multi-electron picture V 1 2 I V 2 2 q × U 2/3 00 01 10 11 ε 0 2 U +
Hydrogen Molecule/Quantum Dots : a a b b a b a t H b t ε = Hamiltonian for 2 separate atoms/dots: t + t - b In total we have 16(2 4 ) states { } { } { } { } { } 0000 1 0001 4 0011 6 0111 4 1111 1 We shall concentrate on the 2-electron problem aa bb ab ba ab ab 2 a b + Hamiltonian with the down-spin level*: a b a b a t b t H a t b t = *empty spots in the matrices will mean 0 now onwards aa bb ab ba ab ab 2 U + 2 U + 2 2 2 2 t t t t t t t t aa bb includes a spin flip process, we are considering only tunneling processes here, so we put 0

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Eigen Values: Obvious ones: 2 ε ab ab To solve rest of the Hamiltonian analytically, we define
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Unformatted text preview: following linear combinations: 1 1 1 2 1 1 B A aa bb - 1 1 1 2 1 1 S T ab ba - We get*: B A S T 2 2 2 2 2 2 A B S T A U B U t S t T + + 2 2 2 2 2 2 B U t A U S t T + + 1 1 1 1 1 1 1 1 1 2 2 aa bb ab ba S T B aa t t ab A bb t t ba t -- = * 2 2 U + ab ab 2 ab ba-( 29 * 2 2 ab ba aa bb + + + 2 t U ∼...
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2009.04.22-ECE659-L38-notes - following linear combinations...

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