Download Lecture 23: Quantum Physics - Wave-Particle Duality and Uncertainty Principle and more Study notes Physics in PDF only on Docsity!
4/16/08 U. W. Physics 104, Spring 2008 1
Lecture 23: Quantum Physics
- Electron diffraction
- Compton Effect
- Uncertainty Principle 4/16/08 U. W. Physics 104, Spring 2008 2
Main point from the last lecture
Light is massless particle and a wave at the same time Electron is a massive particle and a wave at the same time Both interpretations are valid simultaneously because of quantum mechanics 4/16/08 U. W. Physics 104, Spring 2008 (^3)
Electrons are waves
The act of “looking” affects the outcome of the experiment 4/16/08 U. W. Physics 104, Spring 2008 (^4)
Schrodinger’s Cat
• Place cat in box with some poison. If we
don’t look at the cat it will be both dead and
alive!
Poison
Wave nature of particles
• It is a wave of “probability amplitude
distributions”
• The fact that particles “could have” gone
through either slits in Young’s interference
setup (if you did’t look) leads to
interference
• Quantum Mechanics is: a consistent set of
rules on how to account for these
probabilities in agreement with obsevations
4/16/08 U. W. Physics 104, Spring 2008 5 4/16/08 U. W. Physics 104, Spring 2008 (^6) So far only for photons, but De B postulated that it holds for any object with momentum- an electron, a nucleus, an atom, a baseball,…... Should be able to see interference and diffraction for material particles!!
De Broglie Waves
4/16/08 U. W. Physics 104, Spring 2008 7 Photon with energy E=1eV: What about an electron with 1eV (non-relativistic) kinetic energy? Find λ = 1.23 nm for a 1eV electron Big difference!
Wavelength of Electrons
Solve for 4/16/08 U. W. Physics 104, Spring 2008 8
X-Ray Diffraction (Bragg’s Law)
Note: Angle is measured with respect to the horizontal 4/16/08 U. W. Physics 104, Spring 2008 (^9)
Structure of Biological Molecules
X-Ray diffraction from DNA Rosalind Franklin’s picture 4/16/08 U. W. Physics 104, Spring 2008 (^10) A stone is dropped from the top of a building. What happens to the de Broglie wavelength of the stone as it falls?
**1. It decreases
- It stays the same
- It increases Speed, v, KE=mv**^2 /2, and momentum, p=mv, increase.
De Broglie Question
4/16/08 U. W. Physics 104, Spring 2008 (^11)
De Broglie Question
Compare the wavelength of a bowling ball
with the wavelength of a golf ball, if each
have 10 Joules of kinetic energy.
1) λbowling > λgolf
2) λbowling = λgolf
3) λbowling < λgolf
4/16/08 U. W. Physics 104, Spring 2008 (^12)
Compton Scattering
4/16/08 U. W. Physics 104, Spring 2008 19 The precise statement of Heisenberg Uncertainty Principle: Of course if we try to locate the position of the particle along the x axis to Δ x we will not know its x component of momentum better than Δ px, where and the same for z.
QM Summary
• Light and matter are simultaneously waves
and particles (interfere, recoil)
• Planck constant h
• Wavelength is related to momentum
and are conserved (De Broglie)
• Waves of distribution of probability
amplitudes
• Act of observation modifies the probable
outcome
• Uncertainty principle
4/16/08 U. W. Physics 104, Spring 2008 20 4/16/08 U. W. Physics 104, Spring 2008 (^21)
Preflight
According to the Heisenberg Uncertainty
Principle, if we know the x-position of a
particle, we can not know its
- y-position
- x-momentum
- y-momentum
- energy
