What is magnetic diffraction and focussing of electron beams? What are the differences in resolving power between optical and electron microscopes?
Heisenberg’s Uncertainty Principle (See also the separate page on this topic.) Heisenberg’s Uncertainty Principle follows from a classical result, which is at least as old as Fourier. I prefer to introduce it as the Musician’s Uncertainty Principle. When musicians tune up, we listen to the note for a long time so that we can adjust the frequency precisely. We tune by removing beats. (See What are interference beats?) If the frequency difference is one Hz, then you hear an interference beat every second. So, roughly speaking, if the frequencies differ by Δf, then you need a time of 1/Δf to notice. In other words: Δf.Δt > ~ 1 (time taken to measure f) times (error in f) is about one or greater. Musicians know this: if the chord is short, or if you are playing a percussive instrument, the tuning is not as critical. In a long sustained chord, you have to get the tuning accurate. Now in quantum mechanics and atomic physics, the energies of photons are hf, where h is Planck’s constant. So in
