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This is a good opportunity to make use of the natural units in the problem. Here the natural units are $eV$ for energy and $nm$ for distances (assuming this is an atomic problem). If you look at the formula given in the link you have $$T=\frac{1}{1+ \left( \frac{K_2^2 + K_1^2}{2 K_1 K_2} \right)^2 \sinh^2 K_2a}$$ with $K_1 = \sqrt{\frac{2 m E}{\hbar^2}}, \, ...


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Here is what tunneling is about, simplified: According to classical physics, a particle of energy E less than the height U0 of a barrier could not penetrate - the region inside the barrier is classically forbidden. But the wavefunction associated with a free particle must be continuous at the barrier and will show an exponential decay inside the ...


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$T$ and $R$ are transmission and reflection coefficients for waves. They refer to the probability that an incident wave will penetrate the barrier and continue propagating infinitely far. Physically, you should think of it as sending a constant sine wave in from the far left and looking to see what amplitude of constant sine wave you get at the far right. ...



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