1. PH 103 Dr. Cecilia Vogel Lecture 18

2. Review Outline  What is quantization?  Photon  Two pieces of evidence:  blackbody radiation  photoelectric effect  Duality  Wave and particle  Light and matter  REMINDER – EXAM #2 NEXT WED  relativity and quantum

3. What Is Light, Anyway?  Is light a wave?  It diffracts  It interferes  Has polarization  Light shows wave properties  Or is it a particle?  blackbody radiation  photoelectric effect  Compton scattering  Light shows particle properties Wave-particle duality:  Light can show wave or particle properties, depending on the experiment.

4. Wave-particle Duality  Is light a wave?  Light shows wave properties when propagating from point A to point B  Or is it a particle?  Light shows particle properties when interacting with other particles

5. When do We See Which?  Two-slit experiment  Light will propagate through both slits  and waves through slits interfere with each other, but  when it strikes the screen,  it interacts with the screen one photon at a time.

6. Matter  Matter particles, like electrons, have particle properties (of course)  individual, indivisible particles  energy & momentum

7. Duality of Matter  Matter particles, also have wave properties!  They diffract!  They interfere!  Diffract from a crystal, interference pattern depends on  crystal structure ...from a powder, pattern depends on  molecular structure http://hyperphysics.phy-astr.gsu.edu/hbase/davger.html#c1

8. Duality equations  Light/photons  Matter, e.g. electrons Same eqns Only for light Cue: ‘c’ without ‘m’ Only for matter Cue: ‘m’

9. Example What is the wavelength of an electron which has 95 eV of kinetic energy? Note: K<<m o c 2, so we can use classical equations. Note: DO NOT USE E=hc/.

10. Units tips  Use one consistent set of units  SI units OR relativity-friendly units  do not mix  explosion hazard!  You know h and c individually  also useful:  the product hc = 1240 eVnm  useful in light eqns  If all else fails, convert everything to SI

11. Wavefunction  For light, the wavefunction is E(x,t)  electric field (and B(x,t) = magnetic field).  For matter the wavefunction is  (x,t)  like nothing we’ve encountered before.  How does one determine the behavior of the wavefunction?  The Schroedinger equation  Plays the role of F = ma.

12. Wavefunction Interpreted  For light, where the wavefunction (E- field) is large,  the light is bright  there are lots of photons  For matter particles, where the wavefunction is large  there are lots of particles  For an individual photon or matter particle, the wavefunction only tells  probability that the particle will be there  cannot tell where you will find the particle

13. When do We See Which?  In this demo,  For a beam of many particles,  many particles strike the points of constructive interference, where wave is large  Considering a single particle,  each particle is likely to strike a point of constructive interference, where wave is large

14. Position Uncertainty  A wave is not at one place.  For example: water wave hitting the shore, light wave from a source, and yes, matter wave, too   x = uncertainty in position  = spread in positions where the wave is. xx

15. Momentum Uncertainty  A wave is not moving in just one way.  For example sound waves spreading out around the room, light from a bulb, and yes, matter wave, too   p = uncertainty in momentum  = spread in ways the wave moves. pp