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. • In the past several years, subtle experiments have
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This note was uploaded on 01/05/2012 for the course PHYS 107 taught by Professor N/a during the Spring '08 term at University of Wisconsin.

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Phy107Lect27 - From Last Time Heisenberg Uncertainty...

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