Friday 915

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4/36 Friday 9/15
Problem Set PS 1 Today 500PM Today Double
slit experiment Dual behavior particle -
wave
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Wave property

• Interference of waves

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Wave property

• Interference of waves

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Electron interference (1961)

• Modern experiment with electrons

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Interference

• In a modern experiment (1989) with electrons, one
  can shoot one electron at the time or all at
  once. The final pattern is the same
• Tonomura, A., Endo, J., Matsuda, T, and Kawasaki,
  T, Am. J. Phys., 57,117-120 (1989)

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Interference

• In a modern experiment (1989) with electrons, one
  can shoot one electron at the time or all at
  once. The final pattern is the same
• Tonomura, A., Endo, J., Matsuda, T, and Kawasaki,
  T, Am. J. Phys., 57,117-120 (1989)

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Electron or light interference (1943)

• Another experiment with electrons or red light

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Dual behavior of light

• Light can behave as a wave like in the
  interference and diffraction of light
• Light can behave as particles like in the
  photoelectric effect
• Wave-Particle duality of light
• Can particles behave as waves?

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De Broglie (1924)

• If particles can behave as waves, what is the
  wavelength associated with a particle?
• From relativity we know that massless photons
  carry momentum.

• De Broglie proposed that the wavelength
  associated with a particle of momentum p should
  be

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Quantization of angular momentum 2 p R n l
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Diffraction
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X-ray and electron diffractionDavisson and
Germer (1925)

• Diffraction patterns using X-rays or electrons

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Particle-Wave Duality

• Particle-like
• p

• Wave-like
• EM
• Waves
• Matter
• particles

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Heisenberg Uncertainty Principle(1926)

• One cannot measure the position X and the
  momentum in the x-direction with infinite
  accuracy ( and ) at
  the same time.
• If we are able to increase the accuracy in
  position
• , , t he accuracy in momentum
  will decrease
• , , in such a way that

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A measurement introduces indeterminacy
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Consequences

• In classical mechanics, both the momentum and
  position are known at the same time. And with
  the use of Newtons equations, we can predict
  the future of the particle.

• The classical idea of a particles trajectory is
  incompatible with the Heisenberg principle!
• Therefore the Bohr model is incompatible too.

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A new equation

• What is the equation of particle behaving as a
  wave?
• We need an equation that includes the Heisenberg
  and the de Broglie principles.

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Schrödinger EquationQuantization as an
eigenvalue problem(1926)

• Time dependent and time independent
• Schrödinger, E., Ann. Phys. 79, 361 (1926)

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X-ray diffraction

• Diffraction patterns using X-rays

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X-ray diffraction

• Diffraction patterns using X-rays