1. PH 301 Dr. Cecilia Vogel Lecture 11

2. Review Outline  matter waves  uncertainty  Schroedinger eqn  requirements  Another piece of evidence for photons  Compton scattering  Duality

3. Wave Function  A simple wave function is a sinusoidal function of x and t.  This describes a particle with momentum  p=h/.  But where is this particle?  the wavefunction is large everywhere  the particle is everywhere!

4. Wavepackets  Localized wavefunctions can be concocted by  summing sinusoidal functions of different wavelength  i.e. different momenta  Called Fourier synthesis  any well-behaved function can be synthesized in this way

5. 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

6. 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. and/or spread in wavelengths pp

7. Heisenberg Uncertainty Principle What it means:  You cannot know position and momentum both very precisely at the same time  If you measure momentum, you disturb the position, so you no longer know the position accurately -- and vice versa  This disturbance is random, indeterminate ( unlike letting a little air out when you measure the tire pressure)

8. Heisenberg Uncertainty Principle

9. Zero-point motion:  Any confined particle cannot have a definite momentum  in particular, it cannot have zero momentum  any confined particle will have some momentum -- some “zero-point motion”  absolute zero (0 K) cannot be reached

10. Heisenberg Uncertainty Principle What it does not mean:  It does not mean you can’t measure position ( or momentum) very precisely.  It does not mean you need better measuring instruments.  It does NOT just a matter of not knowing: If  x is large enough, an electron will pass thru both of two slits and interfere with itself

11. Another Uncertainty Principle  What it means  If you only have a small time  t to measure energy, you can’t accurately measure energy.  If a particle only lives for a short time  t, you can’t accurately measure its energy.  Since E=mc 2, you can’t accurately measure its mass!  For a short enough period of time  t, you can violate conservation of energy by  E.

12. Example Suppose the rest mass of a particle is 1200 MeV/c 2, and its lifetime at rest is 410 ns. A) Find the uncertainty in its rest energy, due to the fact that you only have 410 ns to measure it. B) Find the uncertainty in its rest mass. C) Is this a substantial fraction of its rest mass? No