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I was just looking over a past homework problem and found something I'm not too sure on -

A particle is in the ground state of a Harmonic potential V (x) = 0.5mω

^{2}x

^{2}

If you measured the energy, what are the possible results, and with what

probabilities?

Now I know the answer to this is 0.5*hbar*ω and 100%. But I'm just a bit confused about when the formula for calculating this energy value can be applied.

E = 0.5*hbar*ω(n+0.5)

When can we use that? ^ Is it just for quantum harmonic oscillators or is it for all Quantum systems?

Cheers