If a classical harmonic oscillator can be at rest, why can the quantum harmonic oscillator never be at rest? Does this violate Bohr's correspondence principle?

In classical mechanics, a harmonic oscillator can be at rest when its velocity and kinetic energy become zero. However, in quantum mechanics, a harmonic oscillator is governed by the wave-like nature of particles and the Heisenberg uncertainty principle, which prevents it from having both zero position and momentum uncertainty. This results in a minimum energy called the zero-point energy, which ensures that the quantum harmonic oscillator can never be at rest. Bohr's correspondence principle states that quantum mechanics should resemble classical mechanics when quantum effects become negligible or in the limit of large quantum numbers. Comparing quantum and classical harmonic oscillators, we find that the probabilities of the quantum harmonic oscillator coming to rest approach classically allowed behavior in this limit. Thus, the inability of a quantum harmonic oscillator to be at rest does not violate Bohr's correspondence principle.