If V0 = 4 eV, E = 1 eV and L = 0.01 nm, determine the probability of a quantum-mechanical electron making its way through this barrier. Express your answer as a percentage. Note: You are being asked to provide a precise calculation, using correct boundary conditions at x = 0 and x = L, and not to use an approximation
If V0 = 4 eV, E = 1 eV and L = 0.01 nm, determine the probability of a quantum-mechanical electron making its way through this barrier. Express your answer as a percentage. Note: You are being asked to provide a precise calculation, using correct boundary conditions at x = 0 and x = L, and not to use an approximation
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If V0 = 4 eV, E = 1 eV and L = 0.01 nm, determine the probability of a quantum-mechanical
electron making its way through this barrier. Express your answer as a percentage.
Note: You are being asked to provide a precise calculation, using correct boundary conditions at x = 0 and x = L, and not to use an approximation.
Hints for part d) of question 4: The required calculation is very similar to the calculation of the
transmission coefficient T for the Finite Potential Barrier given in lectures, but with a different
wavenumber in the region to the right of the barrier.
After applying the boundary conditions at x = 0 and x = L, you may choose to simplify the
expression you find for the transmission coefficient, T. In doing this a useful result is that the
modulus-squared of
f = αβ e−kLˆ
− α
∗β
∗
e
kLˆ
,
where α ≡ ˆk + ik and β ≡ ˆk + iq, is given by
|f|
2 = 4(ˆk
2 + k
2
)(ˆk
2 + q
2
) sinh2
(
ˆkL) + 4ˆk
2
(k + q)
2
.
You may use this result to obtain your answer.
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