Quantum mechanics introduces phenomena that defy classical intuition, one of which is quantum tunneling. This process allows particles to pass through potential energy barriers they seemingly lack the energy to surmount, grounded in the probabilistic nature of quantum mechanics. Unlike macroscopic objects, subatomic particles such as electrons can 'tunnel' through barriers due to their wave-like properties.
A particle's wave function, which provides a probability distribution of its position, can extend beyond barriers, giving a non-zero probability that the particle will be detected on the other side. This does not imply breaking through barriers, as seen in classical mechanics, but vanishing on one side and appearing on the other due to the probabilistic tunneling event, occurring without any intermediate state or path connecting the initial and final positions.
The macroscopic applicability remains negligible under normal circumstances, constrained by factors such as barrier width, particle mass, and energy. For instance, quantum tunneling is pivotal in phenomena like nuclear fusion in stars, where particles overcome electric repulsion barriers at rates unmatched by classical predictions. Despite its profound implications, the concept of human-scale objects tunneling through walls remains improbable within current physical constraints due to their relatively immense mass and the substantial thickness of walls when compared to atomic scales.
In practical terms, advancements in technologies like scanning tunneling microscopes capitalize on tunneling to achieve atomic-resolution imaging, demonstrating the real-world relevance of quantum tunneling within atomic and subatomic frameworks.