A particle has its wave function as the ground state of the harmonic oscillator. Suddenly the spring constant doubles (so the angular frequence dobules). Find the propability that the particle is afterwards in the new ground state. I did solve this, it was quite easy. But doing so I encountered a problem I could really explain - I think it's pretty basic problem but I can't explain it to myself.(adsbygoogle = window.adsbygoogle || []).push({});

You can do two things: You can express the wave function (the old ground state in terms of the new angular frequence) in terms of the new angular frequency and then integrate that with the new ground state to get the probability amplitude.

Or you can express the new ground state in terms of the old angular frequence and integrate up to get the probability amplitude. Either way you get the correct answer.

What my problem was, is that I can't explain that the two procedures are equivalent. It should be pretty basic, after all it is just a matter of which angular frequence you choose to work with. But I still find it a bit miracolous that in the end you get the same... Please explain :)

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# Harmonic oscillator

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