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I have a tiny question that has confused me.

Currently I'm reading about potential wells, harmonic oscillators, the free particle in quantum physics.

If I just take the particle in a box as an example you have a region where the potential is zero, and you have some walls/boundaries where the potential is infinite, so the particle cannot escape.

The energy levels of the particle in a box is given by:

E_{n}= p_{n}^{2}/ 2m,

for n = 1, 2, 3...

So far so good.

But when I get to the harmonic oscillator, the energy levels is given by:

E_{n}= (n + ½)h-bar*ω,

for n = 0, 1, 2...

And then my book just writes: "Note that the ground level of energy in the harmonic oscillator is n = 0, not n = 1..."

So my question is, why is that ? Any particular reason, or just something I have to accept ? :)

Thanks in advance.

Regards

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# Ground level energies (Particle in a box vs Harmonic Osc.)

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