2009.02.11-ECE659-L13-notes

2009.02.11-ECE659-L13-notes - ECE 659 Quantum Transport:...

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ECE 659 Quantum Transport: Atom to Transistor Lecture 13: Differential to Matrix Equations Supriyo Datta Spring 2009 Notes prepared by Samiran Ganguly
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S D L Vd E μ2 μ1 ( 29 2 2 p E U x m = + Time dependent Schrodinger Equation 2 1 2 i i U t m x ψ = - + Time independent Schrodinger Equation E H φ = Hamilton’s equations D(E) 1 p k dx E dt k dk E dt x = = = - If U is constant then the solution is Et i ikx e e - iE t ik x → - then 2 2 2 k E U m = +
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Time independent Schrodinger equation with a space dependent potential op E H Φ = Φ In matrix version { } [ ] { } E H φ = Column vector Square matrix n a n n m m m E H = t t t H t ε = ⋱ ⋱
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This note was uploaded on 01/30/2011 for the course ECE 659 taught by Professor Staff during the Spring '08 term at Purdue University-West Lafayette.

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2009.02.11-ECE659-L13-notes - ECE 659 Quantum Transport:...

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