RE: [math-fun] Items from the most recent AMS journals
Yes, "Uncertainty Principle" sounds good, as long as it's made clear that it's not Heisenberg's Uncertainty Principle. I didn't want to quibble over exactly what constant appears in the RHS, but a precise statement is that if f(x) and F(p) are normalized so that int(|f(x)|^2 dx) = int(|F(p)|^2 dp) = 1, if |f(x)|^2 and |F(p)|^2 are interpreted as probability densities in their respective spaces, and if DeltaX and DeltaP are the respective standard deviations, then DeltaX * DeltaP >= hbar/2. A Gaussian function achieves the minimum uncertainty product. The ordinary uncertainty principle relates position with spatial frequency (or wavelength) or time with frequency. The Heisenberg uncertainty principle relates position with momentum or time with energy. The identification of spatial frequency with momentum or of frequency with energy is possible only within quantum mechanics. Gene Salamin __________________________________________________ Do you Yahoo!? Yahoo! Mail Plus - Powerful. Affordable. Sign up now. http://mailplus.yahoo.com
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Eugene Salamin