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is the formula T = e^-2(alpha)a

where alpha = ((2m(V-E))^1/2)/h

or is it T = 16(E/V)[ 1-E/V]e^-2[(alpha)(a)]?

my book seems to have the second formula but Ive seen online solutions using the first formula

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  • $\begingroup$ Please use Mathjax on this site. It is the site standard for mathematics. $\endgroup$ May 1, 2020 at 12:19

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The general solution for the tunneling probability is: $$ T = \frac{|F|^{2}}{|A|^{2}} $$ Where F is the amplitude of the transmitted complex wave and A is the amplitude of the complex wave incident on the potential barrier. The second equation you shared seems to be an approximation used in the case of a rectangular potential barrier where $ E < V_0 $ (http://tuttle.merc.iastate.edu/ee439/topics/tunneling.pdf). The exact expression for T is a bit more complicated. I would assume the first equation you mentioned would be used in an attempt to further simplify the solution, neglecting the prefactor and highlighting the exponential decay $e^{-2{\alpha}a}$.

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