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Lect08 - We choose to examine a phenomenon which is...

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Lecture 8, p 1 “We choose to examine a phenomenon which is impossible, absolutely impossible , to explain in any classical way, and which has in it the heart of quantum mechanics. In reality, it contains the only mystery.” --Richard P. Feynman
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Lecture 8, p 2 Lecture 8: Introduction to Quantum Mechanics Matter Waves and the Uncertainty Principle
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Lecture 8, p 3 This week and next are critical for the course: Week 3, Lectures 7-9: Week 4, Lectures 10-12: Light as Particles Schrödinger Equation Particles as waves Particles in infinite wells, finite wells Probability Uncertainty Principle Midterm Exam Monday, Feb. 14. It will cover lectures 1-11 and some aspects of lectures 11-12. Practice exams: Old exams are linked from the course web page. Review Sunday, Feb. 13, 3-5 PM in 141 Loomis Office hours: Feb. 13 and 14
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Lecture 8, p 4 This week and next are critical for the course: Week 3, Lectures 7-8: Week 4, Lectures 9-11: Light as Particles Schrödinger Equation Particles as waves Particles in infinite wells, finite wells Probability Uncertainty Principle Midterm Exam Monday, Sep. 20. It will cover lectures 1-9 and some aspects of lectures 10-11. Practice exams: Old exams are linked from the course web page. Review Sunday, Sep. 19, 3-5 PM in 228 Natural History. Office hours: Sep. 19 and 20.
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Lecture 8, p 5 Last Time The important results from last time: Quantum mechanical entities can exhibit either wave-like or particle-like properties, depending on what one measures. We saw this phenomenon for photons, and claimed that it is also true for matter ( e.g. , electrons). The wave and particle properties are related by these universal equations: E = hf Energy-frequency (= hc/ λ only for photons) p = h/ λ Momentum-wavelength
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Lecture 8, p 6 Today Interference, the 2-slit experiment revisited Only indistinguishable processes can interfere Wave nature of particles Proposed by DeBroglie in 1923, to explain atomic structure. Demonstrated by diffraction from crystals – just like X-rays! Matter-wave Interference Double-slit interference pattern, just like photons Electron microscopy Heisenberg Uncertainty Principle An object cannot have both position and momentum simultaneously. Implications for measurements in QM Measuring one destroys knowledge of the other.
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Lecture 8, p 7 Two Slit Interference: Conclusions Photons (or electrons …) can produce interference patterns even one at a time ! With one slit closed, the image formed is simply a single-slit pattern. We “know” ( i.e. , we have constrained) which way the particle went. With both slits open, a particle interferes with itself to produce the observed two-slit interference pattern. This amazing interference effect reflects, in a fundamental way, the indeterminacy of which slit the particle went through. We can only state the probability that a particle would have gone through a particular slit, if it had been measured.
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