# Confusion in Barrier Tunelling formula for physics

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

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

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 $$e^{-2{\alpha}a}$$.