Phy107Lect27 - From Last Time Heisenberg Uncertainty...

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Wed. Nov 10 Phy107 Lecture 27 From Last Time… Heisenberg Uncertainty principle Arises from wave nature of particles. Particle cannot have precise position and momentum. Highly accurate momentum (wavelength) means position is uncertain Can localize particle by superimposing many wavelengths, so momentum is uncertain. Quantum mechanical tunneling. Δ x Δ p
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Wed. Nov 10 Phy107 Lecture 27 The wavefunction and quantum ‘jumps’ Saw that particle has only certain discrete quantum states in which it can exist. Each quantum state has distinct wavefunction, which extends throughout all space It’s square gives probability of finding electron at a particular spatial location. When particle changes it’s quantum state, wavefunction throughout all space changes.
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Wed. Nov 10 Phy107 Lecture 27 Example: hydrogen atom n =1 n =2 n =3 n =4 Photon emitted hf = E 3 -E 1 Wavefunction changes from 3 p to 1 s throughout all space.
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Wed. Nov 10 Phy107 Lecture 27 Example: ‘Particle’ wavepacket Original wavefunction of moving particle A measurement determining particle location to within Δ x Δ x Resulting wavefunction
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Wed. Nov 10 Phy107 Lecture 27 Double-slit particle interference Wave propagates through both slits. Film records point impact, building up interference pattern. Impact point determined probabilistically from wavefunction
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Wed. Nov 10 Phy107 Lecture 27 Measuring the wavefunction Measure induced current from moving charged particle Suppose we measure which slit the particle goes through? Interference pattern is destroyed! Wavefunction changes instantaneously over entire screen when measurement is made.
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Wed. Nov 10 Phy107 Lecture 27 Interference one at a time Attenuated candle – one photon at a time through slits Interference still seen! Conclusion each photon goes through both slits. Experiment with 3 months exposure G.I. Taylor 1909 filter
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Wed. Nov 10 Phy107 Lecture 27 What does Quantum Mech. Mean? Particle going through slits, interference pattern. Probability of hitting screen. But when it is detected, it has hit in one particular place. Don’t measure half an electron, or 0.1 electron. How does this happen?
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Wed. Nov 10 Phy107 Lecture 27 Measurement and interactions Suggests that the measurement is changing the wavefunction. We will see that this may be true in some sense, but not the most obvious one.
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