Answer
The higher the barrier, the lower the probability for the particle to tunnel through.
Work Step by Step
According to classical physics, the particle should never make it through the barrier. However, quantum mechanics allows the wavefunction to penetrate into the classically forbidden region. The greater the particle’s energy, the greater the chance that it will be found on the other side of the barrier.
Mathematically, equation 40.42 gives the tunneling probability. We see that if the barrier height $U_o$ increases while the particle energy E stays fixed, the probability decreases, which confirms our physical intuition.
