I'm trying to understand quantum mechanics and I have a problem with the first application. The solution of Schrödinger equation for a step potential https://en.wikipedia.org/wiki/Solution_of_Schr%C3%B6dinger_equation_for_a_step_potential
Considering the case $E<V_0$, we have a transmission coefficient $T=0$, so I would interpret it as no particle can enter. But looking at the wave function, we see that inside, it decreases exponentially but it is not zero. So I should have a non-null probability to have a particle inside. I don't understand this form of apparent contradiction, a non-null wave function but a transmission coefficient null.