When a free particle encounters a potential step, the behavior of the particle depends on the energy of the particle and the height and width of the potential step.
If the energy of the particle is lower than the height of the potential step, the particle will be partially reflected and partially transmitted. This is known as the phenomenon of quantum tunneling. Even though the particle does not have sufficient energy to surmount the potential barrier classically, there is a finite probability for the particle to tunnel through the barrier and appear on the other side. The transmitted portion of the wavefunction will have a reduced intensity, while the reflected portion will have an amplitude and phase change.
On the other hand, if the energy of the particle is higher than the height of the potential step, the particle will be transmitted with some probability and will continue moving without any significant reflection. In this case, the potential step does not significantly affect the behavior of the particle.
The probability of transmission and reflection is influenced by the width and shape of the potential step as well. A wider potential step will allow for a higher probability of transmission, while a narrower step will result in a higher probability of reflection.
It's important to note that these descriptions assume the particle is treated as a wave described by the wavefunction in quantum mechanics. The behavior of particles at the quantum level is probabilistic, and the probabilities of transmission and reflection are determined by the wave nature of the particle and the properties of the potential step.