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What are the algebraic steps so that I get F? (This is from a Website about Quantum Mechanical Barrier Penetration)

What are the algebraic steps so that I get F? (This is from a Website about Quantum Mechanical Barrier Penetration)

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What are the algebraic steps so that I get F? (This is from a Website about Quantum Mechanical Barrier Penetration)

 

Solving for the transmission coefficient requires evaluation of the boundary conditions at the barrier surface. Continuity of at X=0 ƏY Continuity of at X=0 дх at x = d A+B=C+D ikA-ikB=aD-αC Ce-ad+De+ad ₂+ad = Feikd Continuity of ƏY (αD)e+ad -(αC)e¯ad = ikFeikd Continuity of at X = d Әх The equations can be divided through by A since it sets the scale for the other amplitudes. That gives four equations with four unknowns which can be solved by repeated substitutions. The resulting single equation for the transmission coefficient can be expressed in terms of the known parameters of the barrier.
Transcribed Image Text:Solving for the transmission coefficient requires evaluation of the boundary conditions at the barrier surface. Continuity of at X=0 ƏY Continuity of at X=0 дх at x = d A+B=C+D ikA-ikB=aD-αC Ce-ad+De+ad ₂+ad = Feikd Continuity of ƏY (αD)e+ad -(αC)e¯ad = ikFeikd Continuity of at X = d Әх The equations can be divided through by A since it sets the scale for the other amplitudes. That gives four equations with four unknowns which can be solved by repeated substitutions. The resulting single equation for the transmission coefficient can be expressed in terms of the known parameters of the barrier.
Expert Solution
Step 1: Determine the given variable:

straight A plus straight B equals straight C plus straight D space space space.... left parenthesis 1 right parenthesis ikA minus ikB equals straight alpha straight D minus straight alpha straight C space space space space.... left parenthesis 2 right parenthesis space Ce to the power of negative straight alpha straight d end exponent plus De to the power of plus straight alpha straight d end exponent equals Fe to the power of ikd space space space space space.... left parenthesis 3 right parenthesis left parenthesis straight alpha straight D right parenthesis straight e to the power of plus straight alpha straight d end exponent minus left parenthesis straight alpha straight C right parenthesis straight e to the power of negative straight alpha straight d end exponent equals ikFe to the power of ikd space space.... left parenthesis 4 right parenthesis

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