What is the lowest possible energy of a quantum mechanical system called?

The lowest possible energy of a quantum mechanical system is called zero-point energy.

In classical physics, an object at the bottom of a potential well could be completely motionless and have zero kinetic energy. Quantum mechanics forbids this exact state because the Heisenberg uncertainty principle prevents position and momentum from both being perfectly definite. As a result, even a system in its ground state retains a minimum amount of energy.

For a quantum harmonic oscillator, the zero-point energy is one-half of the oscillator’s quantum of energy, written as ½ℏω. It is not the same as thermal energy: thermal energy comes from temperature-dependent excitation, while zero-point energy remains even at absolute zero. The term ground-state energy is often used in the same context, although zero-point energy emphasizes the residual energy that cannot be removed.

This effect has measurable consequences. Molecular vibrations retain zero-point motion, and liquid helium does not freeze at ordinary pressure even near absolute zero because its quantum fluctuations remain significant. In quantum field theory, the corresponding minimum energy of fields is associated with vacuum energy.