Zero Point Energy: Harmonic Oscillator vs Rigid Rotator

[Useful nucleus]

The harmonic oscillator and the rigid rotator are traditional examples in any quantum mechanics text. The former can represent the vibrations of a diatomic molecule while the latter can represent its rotation. By solving the time-independent Schroedinger equation for the two systems, one obtains:
E$_{n}$ = const. (n+$\frac{1}{2}$) , where n=0,1,2,... for the harmonic oscillator, and:
E$_{J}$=const. J(J+1) , where J=0,1,2,... for the rigid rotator.

One can see that in the former case there is zero point energy (at n=0), while in the latter there is not (J=0 $\Rightarrow$ E=0). In one text I came across the following explanation for the appearance of the zero point energy in the harmonic oscillator:
If E=0 , Kinetic energy =0 $\Rightarrow$ momentum=0 AND potential energy =0 $\Rightarrow$ x=0 . Hence, Both Δx=0 and Δp=0 violating the uncertainty principle.

I tried to follow this logic on the rigid rotator for which the potential energy is zero by construction. Hence, E=0 implies p=0 but the position has infinite uncertainty ( I guess it may be better to talk about angular momentum and angle here instead of p, x).

I tried to conclude from this that zero point energy arises from potential energy. For potential-free systems , it should not arise. Am I right in my conclusion? Any insight will be appreciated.

 

[phyzguy]

I tried to follow this logic on the rigid rotator for which the potential energy is zero by construction. Hence, E=0 implies p=0 but the position has infinite uncertainty ( I guess it may be better to talk about angular momentum and angle here instead of p, x).

One comment. In the rigid rotator, if the angular momentum is zero, that means the angle is completely uncertain - it can be anything between 0 and 2 pi.

 

[Useful nucleus]

Thank you for refining my statement, phyzguy! I would improve my statement by saying that E=0 does not violate any form of the uncertainity principle in the ridgid rotator case.

 

[rcttsoul2]

So in laments terms, Zero Point Energy actually comes from the friction from the fabric of space stretching around atoms (causing them to move), and since the universe is continually expanding, it could potentially create an incredible amount of power?

 

[Mark M]

So in laments terms, Zero Point Energy actually comes from the friction from the fabric of space stretching around atoms, and since the universe is continually expanding, it could potentially create an incredible amount of power?

There is no such thing as the 'fabric of space'. You're speaking about curved spacetime in general relativity. This means that the geometry of the spacetime has changed, so that objects trying to follow geodesics end up taking curved paths through spacetime. It certainly does not that space is some kind of fabric.

Zero point energy, as explained in the OP, is a result of the lowest energy state 'n' being non-zero.

 

[rcttsoul2]

So where is this minimal energy coming from, I still believe that energy can't be created or destroyed, I always thought that the miniscule movement of particles was caused by the continued expansion of the universe.
If you could, please explain in laments terms for me.