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Chapter2_28

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

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PHY4604 R. D. Field Department of Physics Chapter2_28.doc University of Florida Quantum Mechanical Tunneling (3) A ik A ik A ik e e e e ikA e e e e ik A e e e e ikA ik A FDet L L L L L L L L L L L L κ κ κ κ κ κ κ κ κ κ κ κ κ κ κ κ κ κ κ κ κ κ κ κ κ 4 2 2 0 0 1 1 1 0 0 0 0 0 0 1 1 1 = + = + + = + + = + + + + + + Thus, ( ) ) cosh( 2 ) sinh( ) ( 2 2 2 L ik L k Ae ik Det FDet F ikL κ κ κ κ κ + = = Transmission Coefficient: The probability that a particle entering from the left will make to into Region 3 is ( ) ( ) ( ) ) ( sinh ) ( 4 4 ) ( sinh ] 4 ) [( 4 4 ) ( cosh 4 ) ( sinh ) ( 4 | | | | 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 L k k k L k k k k L k L k k A F P m k m k T κ κ κ κ κ κ κ κ κ κ κ κ κ κ + + = + + = + = = h h Notice that
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