Yes, physicists have observed and documented cases of electrons in the ground state undergoing quantum tunneling. Quantum tunneling is a phenomenon in quantum mechanics where a particle can pass through a potential energy barrier that it classically should not be able to overcome.
One of the earliest experimental verifications of quantum tunneling involved the observation of alpha decay. Alpha particles are composed of two protons and two neutrons and are emitted by certain radioactive nuclei. According to classical physics, these particles do not possess enough energy to escape the strong nuclear forces holding the nucleus together. However, in quantum mechanics, there is a finite probability for the alpha particles to tunnel through the barrier and escape.
In addition to alpha decay, quantum tunneling has been observed and studied in various other systems, including electrons tunneling through potential barriers in solid-state devices such as tunneling diodes and scanning tunneling microscopy. These experiments provide direct evidence for the phenomenon of quantum tunneling and have been crucial in understanding the behavior of particles at the quantum level.
It is important to note that the ground state of an electron refers to its lowest energy state within an atom or a system. While quantum tunneling is more commonly associated with excited states, it is also possible for electrons in the ground state to tunnel under specific circumstances.