All sorts of quantum systems show tunneling, which means the leaking of a wavefunction through a region in which its kinetic energy is negative. Typical radioactive decays involve tunneling. Many electrical devices require electron tunneling through barriers.

Quantum "leaps" are a fictional process introduced in the early days of proto-quantum theories. In modern quantum mechanics, the quantum state always evolves via a continuous process.There's some mystery involved in the "measurement" aspect of the process, in which we see only a portion of the resulting quantum state, but so far as we know no "leap" ever occurs. If you wish to look up more on this measurement process, a key search term is "decoherence".

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