# Harmonic Oscillator - Zero Point Energy and the Correspondence Principle

I have been studying the harmonic oscillator in quantum mechanics.

I fully understand the origin of the zero-point energy and how it can be mathematically shown using the uncertainty principle that the harmonic oscillator cannot have $0$ energy.

However, on a classical scale, in our daily lives, we can see/imagine zero energy, for example, a ball at rest on the ground.

My question is, how does a quantum system's inability to occupy $0$ energy and our classical 'intuition' of zero-energy relate?

I hope my question is clear.

• The zero-point energy is proportional to $h$... – Valter Moretti Dec 20 '17 at 18:05
• – Qmechanic Dec 20 '17 at 18:13
• @Qmechanic thanks but I don’t feel like it properly answers my question... – PhysicsMathsLove Dec 20 '17 at 19:31
• I don't understand what this zero point energy is supposed to mean since you cannot extract it and absolute energy is meaningless. – DanielSank Dec 21 '17 at 4:59

I'm assuming by zero-point energy you are asking a simple harmonic oscillator problem in the quantum mechanics context. Then that's equivalent to ask how could you go to classical limit of a quantum system. Well, quite simple: by taking $\hbar\rightarrow 0$. Therefore you obtain the zero-point fluctuation vanishes.