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Is there an easy way to explain why pi shows up here?
by brink 7y ago
Is there an easy way to explain why pi shows up here?
- MiroF 7y agoWhen taking the integral over a gaussian distribution, coincidentally the distribution describing a single particle at minimum uncertainty, you get an answer in terms of pi.
- hervature 7y agoNot a physicist, but don't you mean maximum? Gaussian distribution is entropy maximum with finite mean and variance
- evanb 7y agoI am a physicist, and minimum is correct. Quantum uncertainty is not an entropy measure. Importantly, the 'minimum uncertainty' is not just about the width of the wavefunction in position space---the uncertainty principle (roughly speaking) says that the variance in position space times the variance in momentum space has a lower bound. A gaussian saturates that bound.
- xdavidliu 7y agolast time I took grad quantum was Spring 2010, so I need a refresher. What does it mean for a particle to be "at minimum uncertainty"?
- peteradio 7y agoh < dPdX is generally true h = dPdX is case of minimum uncertainty I'm guessing that is what is meant by minimum uncertainty.
- liuhenry 7y agoFull derivation: https://physicspages.com/pdf/Griffiths%20QM/Griffiths%20Problems%2003.16.pdf https://physicspages.com/pdf/Griffiths%20QM/Griffiths%20Prob...