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# Lect07 - Le cture7 I ntroduction to QuantumMe chanics Light...

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Lecture 7, p 1 Lecture 7: Introduction to Quantum Mechanics: Light as Particles f (x10 14 Hz) V stop (v) 0 0.5 1 1.5 2 2.5 3 3.5 0 5 10 15 S 1 S 2 V Collector Metal Surface electrons A

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Lecture 7, p 2 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 Office hours: Feb. 13 and 14
Lecture 7, p 3 Thumbnail Summary of Waves Wave relationships: Wavelength, frequency, speed, amplitude, intensity v = f λ , I = A 2 , etc . 2-slit interference: Phase difference depends on source phases and path lengths. A tot = 2A 1 cos( φ /2), etc . N-slit interference: Diffraction gratings, Rayleigh’s criterion. 1-slit diffraction: Circular apertures, Rayleigh’s criterion, limits on optics. Interferometers. We’ll use many of these results when we study quantum mechanics.

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Lecture 7, p 4
Lecture 7, p 5 Today Photoelectric Effect: Light as particles Photons - Quanta of electromagnetic waves The fundamental QM relations : Energy: E = hf or E = ћ ϖ (ћ = h/2 π and ϖ = 2 π f) Momentum: p = h/ λ These equations relate the wave and particle properties of all quantum mechanical entities. Reading in the text: 38.1-2,9 and 39.1-5 Note: All reading assignments are listed on the syllabus page.

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Lecture 7, p 6 Wave-particle Duality for Light and Matter In Physics 212 and the first 4 Lectures of Physics 214, we considered “light” to be a wave. This was established by experiment in the 19 th century (cf. Poisson spot) Electromagnetic waves exhibit interference and diffraction. Surprise : In the early 20 th century, it was discovered that light has particle-like properties ( e.g. , localized lumps of energy) in some situations! Furthermore, matter exhibits wave-like properties ( e.g. , electrons, protons, etc .) under certain circumstances. It may seem surprising t hat an entity might exhibit both “wave-like” and “particle-like” properties! Let’s look at some of the evidence.
Lecture 7, p 7 Photoelectric Effect (1) Electrons in a metal are bound by an energy Φ , called the work function . If you shine light on a clean metal surface, electrons can emerge the light gives the electrons enough energy (> Φ ) to escape. Measure the flow of electrons with an ammeter. How will the current depend on intensity and frequency? We might expect: Increasing the intensity should increase the current. Or maybe the energy of the electrons. Increasing the frequency shouldn’t matter much. Perhaps a decrease in current due to rapid oscillations. With low intensity , there should be a time delay before current starts to flow, to build up enough energy.

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Lect07 - Le cture7 I ntroduction to QuantumMe chanics Light...

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