Review of EM wave particle EM wave behave as particle: Proof: Blackbody radiation. Plank proposes ??? to solve ??? problem. Photoelectric effect. Einstein proposes ??? in order to explain ???. Compton Scattering. Try to derive Compton Scattering formula ' mhc 1 cos and explain why this is a proof that e photon here behaves as particle. Energy (EM wave) converts into matter (particle) Pair production. D: particle When photon is a particle, a wave? D: wave Particles (matter) behave as waves and the Schroedinger Equation 1. Quiz 9.23. 2. Topics in particles behave as waves: The (most powerful) experiment to prove a wave: interference. today Properties of matter waves. The free-particle Schrödinger Equation door to a different world. The Uncertainty Principle. The not-unseen observer. Thur. The Bohr Model of the atom. 3. The second of the many topics for our class projects. 4. Material and example about how to prepare and make a presentation (ref. Prof. Kehoe) The (most powerful) experiment to prove a wave: interference Particle or wave, how do I know? Particle: scattering. Characterized by mass, position and momentum. Wave: interference. Characterized by wavelength, frequency, amplitude, phase. A double-slit experiment: A review of the double-slit experiment in optics. A nice review article: http://en.wikipedia.org/wiki/Double- slit_experiment. A description of the “thought” experiment: a double-slit experiment with electrons. What is oscillating? The probability density of finding the particle at a certain location and time. The Bragg’s Law The Bragg’s Law for X-rays scattering off a crystal surface – a powerful tool to study crystal structures through diffraction. Constructive interference when: 2dsin m Where m is the order of interference. m = 1, 2, 3, The Davisson-Germer experiment Results: Confirmed that the Bragg Law applies to electrons as well. Electrons interfere. Electrons behave like a wave. Ref: http://hyperphysics.phy-astr.gsu.edu/Hbase/davger.html#c1 Properties of matter waves The de Broglie wavelength of a particle: h p Frequency: f E h (review) Wave number k 2 and angular frequency: 2 T 2 f The h-bar constant: h 2 p k E Discussion about the velocity on the board. The free-particle Schrödinger Equation Waves on a string – a mechanical wave The wave equation (needs classical mechanics) 2 y x,t 2 y x,t y v v 2 x 2 t 2 A solution: the wave function: x y x,t Asin kx t with v k The Electromagnetic waves (Maxwell’s equations): E 0 B 0 B E E B 0 0 t t E Asin kx t ˆ y with c k And the solutions: 1 B Asin kx t ˆ z and 1 c 2 0 0 c The free-particle Schrödinger Equation The matter waves 2 Ψ x,t Ψ x,t 2 i 2m x 2 t The interpretation of the matter wave function probability density = Ψ x,t 2 The plane wave Ψ x,t Aei kxt Review questions How do you understand the wave function of Ψ x,t Please review the mechanical waves you learned in intro level physics course. Refresh yourselve with wavelength, frequency, amplitude, wave energy density, wave phase velocity, wave group velocity. Preview for the next class Text to be read: In chapter 4: Section 4.4 Section 4.5 Section 4.6 Questions: According to the momentum-position uncertainty principle, if you know a particle’s position exactly, what precision can you reach in its momentum measurement? What is Bohr’s atom model? In which what is his main postulate? What is the Bohr radius? Google “electron microscope” and read about it. Can you connect this instrument with what we discuss here?
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