quantum mechanical tunneling
Any standard quantum mechanical book will be able to explain it to you.
I give you a few examples of existence of Quantum mechanical tunneling.
1. Diode with high doping density breaks down in reverse bias due to tunneling of minority careers across the potential barrier to create reverse breakdown effect.
2. Look at the fission process in thermonuclear bomb. it is attributed to tunneling and it conforms with the experimental results.
3. Tunneling diode
4. Tunneling accelerometers: They rely on the tunneling of electrons between two electrodes separated by insulator across which there is a potential barrier.
In terms of quantum mechanics it is the non-zero value of the wave function or more specifically the probability of the field at the field point that comes as a solution of Schrodinger's equation subjected to boundary conditions. It is the boundary conditions that lead to existence of the tunneling field at a point where classical ideas cannot explain it.