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Tunneling is a consequence of the wave nature of matter, where the quantum wave function describes the state of a particle or other physical system, and wave equations such as the Schrödinger equation describe their behavior. The probability of transmission of a wave packet through a barrier decreases exponentially with the barrier height, the barrier width, and the tunneling particle's mass, so tunneling is seen most prominently in low-mass particles such as electrons or protons tunneling through microscopically narrow barriers. Tunneling is readily detectable with barriers of thickness about 1–3 nm or smaller for electrons, and about 0.1 nm or smaller for heavier particles such as protons or hydrogen atoms.[1] Some sources describe the mere penetration of a wave function into the barrier, without transmission on the other side, as a tunneling effect, such as in tunneling into the walls of a finite potential well.

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