The concept of the "zero-point energy of an atom in the ground state" is not an axiom of quantum mechanics, but rather a consequence of the principles and mathematical framework of quantum mechanics itself. It arises from the uncertainty principle and the wave-particle duality inherent in quantum theory.
In quantum mechanics, particles such as electrons are described by wavefunctions that represent the probability amplitudes of finding the particles in different states. According to the uncertainty principle, there is a fundamental limit to the precision with which certain pairs of physical properties, such as position and momentum, can be simultaneously known. This uncertainty leads to fluctuations in the energy of a quantum system, even when it is in its lowest possible energy state, known as the ground state.
These energy fluctuations, arising from the wave nature of particles, give rise to the concept of zero-point energy. The zero-point energy is the minimum energy that a quantum system possesses even at absolute zero temperature (0 Kelvin). It represents the residual energy inherent in a quantum system due to the uncertainty principle.
Experimental confirmation of the existence of zero-point energy comes from various phenomena in quantum mechanics. One notable example is the Casimir effect, which is the attraction observed between two closely spaced parallel conducting plates due to the zero-point energy of electromagnetic fluctuations in the vacuum. The Casimir effect has been experimentally verified and provides indirect evidence for the existence of zero-point energy.
Therefore, while the concept of zero-point energy is not a direct empirical observation, it is a consequence of the principles and mathematical formalism of quantum mechanics, and its existence is supported by experimental evidence such as the Casimir effect.