Experimental evidence for the ground state of energy

[PerpStudent]

I hope this is a coherent question: Solving the Schrödinger equation for energy eigenvalues for a harmonic oscillator leads to the ground state of the energy for a particle being ω/2. What is the experimental evidence that this is, in fact, the lowest achievable energy and that zero energy is not achievable?

 

[The_Duck]

Suppose you have a harmonic oscillator in the ground state, and you slowly increase the value of ω. You will have to do work on the oscillator to accomplish this. The ground state energy changes by (change in ω)/2, so this is the amount of work you have to do on the oscillator.

This is seen in, for example, the Casimir effect: http://en.wikipedia.org/wiki/Casimir_effect

In the Casimir effect, there's basically a harmonic oscillator corresponding to each mode of the electromagnetic field that can exist between the two plates. In general, these oscillators sit in their ground state. Changing the separation of the plates changes the frequencies of these oscillators, changing their ground state energy. So you have to do work in order to move the plates. In other words, there is a force between the plates that you can calculate from W = Fd. This is one way of understanding how the Casimir force arises.

 

[PerpStudent]

Thanks for your response. I see that the observed forces in the Casimir effect are consistent with the quantum theory of the harmonic oscillator. However, is there any experiment that demonstrates that the ground state of the energy for a particle cannot be zero? I understand that a zero ground state energy would be inconsistent with the theory, but I am searching for some experiment that clearly shows that it is impossible to have a zero ground state. Perhaps some experiment performed near absolute zero temperature?