Understanding Photons: Wave-Particle Duality and Probability in Quantum Mechanics, Assignments of Physics

Download Understanding Photons: Wave-Particle Duality and Probability in Quantum Mechanics and more Assignments Physics in PDF only on Docsity! 1 Announcements • HW#5 due today • No new homework for next week. • Class on Friday: Review of SR Yeah!! Today: We will finish our discussion about photons. All these fifty years of conscious brooding have brought me no nearer to the answer to the question, 'What are light quanta?' Nowadays every Tom, Dick and Harry thinks he knows it, but he is mistaken! (Albert Einstein, 1954) Review: Where’s the photon? Great question! But no one can answer it… However: The probability to find photons in a beam of light is largest at places where the light intensity largest. Important conclusion: The probability to find a photon at a specific location in a beam of light is proportional to the intensity of the beam at that location. i.e.: Probability is proportional to E2max How can light behave like a wave (interference etc), but be made up of little chunks (photons) that seem to hit at random places? If I shoot a photon through the two slits to hit the screen, it… a. cannot hit in the middle, because block is in the way. b. is completely random where it can hit. Has equal chance of hitting anywhere on the screen. c. must hit at the maximum of the interference pattern d. has some chance of being anywhere, but on average better chance of being where interference pattern in brightest. e. will hit anywhere it has a straight shot through either slit Which is best answer, and why? (will randomly ask for reasons) Q1: Probability of photon hitting given by where field is biggest (electric field strength)2~Intensity & proportional to the probability of where photon will hit! standard electric field representation of light field Classical electric field wave pattern describes probability of where photons will be… higher intensity, higher likelihood that photon will be detected there. If I shoot a photon through the two slits to hit the screen, it has some chance of being detected anywhere on screen, but on average better chance at being where interference pattern in brightest. Two slit interference 2 Which slit did this photon go through? a. left b. right c. both d. neither e. either left or right we just cannot know which one Q2: Which slit did this photon go through? a. left b. right c. both! d. neither If one slit: Get single slit pattern (i.e. no interference) But: that photon is part of the two slit interference pattern, the probability pattern of where it lands is described by the 2 slit interference pattern, it must have gone through both slits i. e. as a wave! When it interacts with the screen it behaves particle-like! Photon before it goes through the slits Photon as little segment of wave moving towards slits Intensity of wave in various places, indicates probability of finding the photon there if you looked at that moment. Photon after it went through the slits Photon is a wave… It can interfere with itself. Intensity of wave in various places indicates the probability of the photon concentrating at that spot if you had detector (e.g. a bunch of atoms or a sheet of metal) Photon after it goes through the slits Photon is a wave… It can interfere with itself. Intensity of wave in various places indicates probability of the photon concentrating at that spot if you had detector (e.g. a bunch of atoms or a sheet of metal) When photon interacts with an electron or atom, all energy ends up in one spot… Behaves like a particle with energy = hc/λ Randomness in physics??! A completely new concept in QM is that the outcome of a measurement can often times not be predicted precisely. We can only predict the probability of obtaining a certain result! (Randomness is negligible for macroscopic objects but important on atomic scale!) Where will a photon hit the screen? Examples: Well, we don’t know, but the probability is largest where the intensity of the light is largest ∝ (field amplitude)2 Where is the electron in a hydrogen atom? Well, we don’t know, but the probability to find it is largest at the location where the square of the matter wave amplitude is largest. (Matter waves: see TZT chapter 6)