Chapter2_28 - PHY4604 R. D. Field Quantum Mechanical...

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Unformatted text preview: PHY4604 R. D. Field Quantum Mechanical Tunneling (3) +1 −1 − ik − κ FDet = 0 e + κL 0 κe + κL −κ = A e + κL κe +κL +κ e −κL − κe −κL −1 +κ e −κL − κe −κL −A − ikA 0 0 − ik −1 0 + ikA e + κL 0 κe +κL −1 e −κL − κe −κL −1 0 0 = 2ikκA + 2ikκA = 4ikκA Thus, FDet 2ikκAe − ikL F= = Det − (κ 2 − k 2 ) sinh(κL) + 2ikκ cosh(κL) ( ) Transmission Coefficient: The probability that a particle entering from the left will make to into Region 3 is hk | F |2 4k 2κ 2 m PT = hk = | A |2 ((κ 2 − k 2 ) 2 sinh 2 (κL) + 4k 2κ 2 cosh 2 (κL) ) m = = 4k 2κ 2 4k 2κ 2 + [(κ 2 − k 2 ) 2 + 4k 2κ 2 ] sinh 2 (κL) ( 4k 2κ 2 4k 2κ 2 + (κ 2 + k 2 ) 2 sinh 2 (κL) ( ) ) Notice that V02 1 (k 2 + κ 2 ) 2 2 =1+ sinh (κL) = 1 + sinh 2 L 2m(V0 − E ) / h 2 22 PT 4k κ 4 E (V0 − E ) ( ) High-Wide Barrier: In the limit of large κL we have sinh(κL) ≈ 1 e +κL 2 κL >>1 and V02 1 2L e ≈ PT 16 E (V0 − E ) PT ≈ Department of Physics 16 E (V0 − E ) − 2 L e V02 Chapter2_28.doc 2 m (V0 − E ) / h 2 2 m (V0 − E ) / h 2 University of Florida ...
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This note was uploaded on 05/29/2011 for the course PHY 4064 taught by Professor Fields during the Spring '07 term at University of Florida.

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