In quantum mechanics within a finite potential well, the stationary state wave function exhibits exponential decay in regions where the particle's energy is lower than the potential barrier height. This non-zero probability density outside the confinement boundaries implies that particles can traverse barriers without sufficient classical kinetic energy through the mechanism known as quantum tunneling. Consequently, a confined particle possesses a small but finite probability of existing beyond the theoretical walls of its potential well when those walls are not infinitely deep or high.
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Quantum Tunneling in Particle in a Box Potential
In quantum mechanics within a finite potential well, the stationary state wave function exhibits exponential decay in regions where the particle's energy is lower than the potential barrier height. T…