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Unformatted text preview: Lecture 10, p 1 Quantum mechanics is the description of the behavior of matter and light in all its details and, in particular, of the happenings on an atomic scale. Things on a very small scale behave like nothing that you have any direct experience about. They do not behave like waves, they do not behave like particles, they do not behave like clouds, or billiard balls, or weights on springs, or like anything that you have ever seen.Richard P. Feynman Lecture 10, p 2 Lecture 10: The Schrdinger Equation Lecture 10, p 3 This week and last week are critical for the course: Week 3, Lectures 79: Week 4, Lectures 1012: Light as Particles Schrdinger Equation Particles as waves Particles in infinite wells, finite wells Probability Uncertainty Principle Next week: Homework 4 covers material in lecture 10 due on Thur. Feb. 17. We strongly encourage you to look at the homework before the midterm! Discussion : Covers material in lectures 1012. There will be a quiz . Lab: Go to 257 Loomis (a computer room). You can save a lot of time by reading the lab ahead of time Its a tutorial on how to draw wave functions. Midterm Exam Monday, Feb. 14. It will cover lectures 111 and some aspects of lectures 1112. Practice exams: Old exams are linked from the course web page. Review Sunday, Feb. 13, 35 PM in 141 Loomis Office hours: Feb. 13 and 14 Lecture 10, p 4 Overview Probability distributions Schrdingers Equation Particle in a Box Matter waves in an infinite square well Quantized energy levels Wave function normalization Nice descriptions in the text Chapter 40 Good web site for animations http://www.falstad.com/qm1d/ U= (x) L U= n=1 n=2 x n=3 Lecture 10, p 5 Having established that matter acts qualitatively like a wave, we want to be able to make precise quantitative predictions , under given conditions. Usually the conditions are specified by giving a potential energy U(x,y,z) in which the particle is located. Examples: Electron in the coulomb potential produced by the nucleus Electron in a molecule Electron in a solid crystal Electron in a nanostructure quantum dot Proton in the nuclear potential inside the nucleus x U(x) For simplicity, consider a 1dimensional potential energy function, U(x). Matter Waves  Quantitative Classically, a particle in the lowest energy state would sit right at the bottom of the well. In QM this is not possible. (Why?) Lecture 10, p 6 Act 1: Classical probability distributions x P(x) a b c E x U(x) Ball in a box: x P(x) E Ball in a valley: x U(x) a b c HINT: Think about speed vs position. Start a classical (large) object moving in a potential well (two are shown here)....
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This note was uploaded on 04/04/2011 for the course PHYSICS 214 taught by Professor Mestre during the Spring '11 term at University of Illinois at Urbana–Champaign.
 Spring '11
 MESTRE
 mechanics, Magnetism, Light

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