### Overstepping the boundaries: Harmonic Oscillators Defy the Classical Limits

How can parity work for you in quantum mechanics? We see that the parity of the harmonic oscillator solutions can make some problems trivial (the average value of the position, for example). We computed the probability of a harmonic oscillator being stretched or compressed further than classical mechanics would permit, to discover that in the ground state of HCl the probability was 15% that the classical limits would be exceeded.

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