Understanding Uncertainty in Quantum Mechanics: Heisenberg's Principle - Prof. Jean-Pierre, Study notes of Physics

Download Understanding Uncertainty in Quantum Mechanics: Heisenberg's Principle - Prof. Jean-Pierre and more Study notes Physics in PDF only on Docsity! Heisenberg Uncertainty Principle Quantum Mechanics  Heisenberg Uncertainty Principle (HUP)- position and momentum cannot be known simultaneously, to arbitrary high precision.  Uncertainty- referees to measurements; the scale used determines accuracy. Intuitively, accuracy seems to be continuous.  There is a limit to how accurate a measurement can be in nature (Planck’s constant = 10-34) Electron Diffraction - Exhibits wave properties. | Px= 0 Px=MVx | Px=0 ± x/h    (Vertical axis = X))    |  |  Amount of diffraction = / wλ/ w * = wavelength, w= with of slitλ/ w  Can find the amount of the diffraction by the angle at which the dark band is from the horizontal.  De Broglie’s = = h/mvλ/ w y From the above equations we can gather: = (θ = ( h/mvy)/w *Uncertainty lies within the width of the slit, ∆x= w, called ∆px (In the picture it refers to Px as Py, ignore that. Also R is suppose to be Py=mvy) = ∆Pθ = ( x/mvy *Derived from = opposite/adjacent. θ = ( To derive Heisenberg’s Formula from given information:  = (θ = ( h/mvy)/w = ∆Px/mvy = (h/mvy)/∆x  = h/∆x = ∆Pθ = ( x  h = ∆Px ∆x  ∆x∆Px > ħ /2  ^^ must be in order with 10-34  ħ = h/2π