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Unformatted text preview: Lecture 12, p 1 Lecture 12: Particle in 1D boxes, Simple Harmonic Oscillators U →∞ →∞ →∞ →∞ U →∞ →∞ →∞ →∞ x n=0 n=1 n=2 n=3 U(x) ψ (x) Lecture 12, p 2 This week and last week are critical for the course: Week 3, Lectures 79: Week 4, Lectures 1012: Light as Particles Schrödinger 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 – It’s 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 12, p 3 Bound State Properties: Example Bound State Properties: Example Consider these features of ψ : 1: 5th wave function has __ zerocrossings. 2: Wave function must go to zero at ____ and ____ . 3: Kinetic energy is _____ on right side of well, so the curvature of ψ is ______ there. E 5 U= ∞ U= ∞ L x U o x ψ Let’s reinforce your intuition about the properties of bound state wave functions with this example: Through nanoengineering, one can create a step in the potential seen by an electron trapped in a 1D structure, as shown below. You’d like to estimate the wave function for an electron in the 5th energy level of this potential, without solving the SEQ. Qualitatively sketch the 5th wave function: Lecture 12, p 4 Bound State Properties: Bound State Properties: Solution Solution Consider these features of ψ : 1: 5th wave function has __ zerocrossings. 2: Wave function must go to zero at ____ and ____ . 3: Kinetic energy is _____ on right side of well, so the curvature of ψ is ______ there. E 5 U= ∞ U= ∞ L x U o x ψ Let’s reinforce your intuition about the properties of bound state wave functions with this example: Through nanoengineering, one can create a step in the potential seen by an electron trapped in a 1D structure, as shown below. You’d like to estimate the wave function for an electron in the 5th energy level of this potential, without solving the SEQ. Qualitatively sketch the 5th wave function: 4 x = 0 x = L lower smaller ψ and d ψ /dx must be continuous here. The wavelength is longer. Lecture 12, p 5 Example of a microscopic potential well a semiconductor “quantum well” Deposit different layers of atoms on a substrate crystal: AlGaAs GaAs AlGaAs U(x) x An electron has lower energy in GaAs than in AlGaAs. It may be trapped in the well – but it “leaks” into the surrounding region to some extent Quantum wells like these are used for light emitting diodes and laser diodes, such as the ones in your CD player....
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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
 Magnetism, Light

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