Remark on Heisenberg's inequality
YU Hai-bo · Journal of Science of Teachers' College and University · 2007
Let f(t)be absolutely continuous in the interval [-a,a]for any a 0,then(∫-+ ∞∞ |f(t)|2 dt)2≤ 4 u 2v2-A2,where A = 2(x0 u-y0v),u 2=∫-+ ∞∞t2| f(t)|2dt,v 2 =∫-+ ∞∞| f'(t)|2dt,x 0=∫-+∞∞[ f(t)/(1+ t2)π]'dt,x 0 =∫-+ ∞∞[ f(t)/(1+t2)π]'dtand y 0=-+ ∞∞[ f'(t)/(1+t2)π]'dtare all finite.