In classical physics, a particle cannot escape from a potential well if its total energy is less than the potential energy at the bottom of the well. This is due to the conservation of energy, which states that the total energy of a system remains constant over time.
When a particle is trapped in a potential well, it experiences a force that brings it back towards the bottom of the well. If the particle's energy is insufficient to overcome the potential energy barrier at the bottom, it will continue to oscillate within the well indefinitely.
However, in quantum mechanics, there is a phenomenon called quantum tunneling that allows particles to pass through potential barriers even if their energy is lower than the barrier height. According to the principles of quantum mechanics, particles can exhibit wave-like properties and have a probability of "tunneling" through energy barriers.
In quantum tunneling, there is a finite probability that a particle can appear on the other side of an energy barrier, even if it doesn't have enough energy to classically overcome it. This phenomenon is essential in various fields of physics, such as nuclear decay, scanning tunneling microscopy, and semiconductor devices.
So, while in classical physics a particle cannot escape from a potential well if its energy is insufficient, in quantum mechanics, there is a non-zero probability that the particle can tunnel through the barrier and escape.