Matter Waves. Byungsung O Department of Physics, CNU x6544
|
|
- Arabella Dawson
- 5 years ago
- Views:
Transcription
1 Matter Waves x6544
2 Electrons and Matter Waves If electromagnetic waves (light) can behave like particles (photons), can particles behave like waves? forwaves, then forparticles (de Broglie wavelength) x-ray diffraction electron diffraction
3 De Broglie wavelength What is the de Broglie wavelength for anelectron with =120 ev? = MeV : non-relativistic ㆍ kgㆍm/s m =0.112 nm = 112 pm
4 Wavefunctions To describeamatterwave, wavefunction In all the situation, where ()is theangularmomentum What does the wavefunction mean? A matterwaveisaprobabilitywave: theprobability that a particle will be detected in a specific time interval is proportional to (which isreal and non-negative) ( ):probabilitydensity
5 How do we find the wavefunction? Sound waves / waves on strings: Newton's equation Light waves: Maxwell's equation Matter waves: Schro"dinger's equation Schro"dinger's equation ( )
6 Schro"dinger's equation for a free particle Freeparticle: and or The general solution with travelling travelling +x direction -x direction [Any ± representsatraveling wave]
7 Wavefunction for a free particle Assumeafreeparticleis movingin thepositivedirection of The probability density (aconstant) Prob. density is thesameforall. Theparticlehas equal prob. of being anywherealong axis
8 Uncertainties In the previous example, the momentum is exactly defined but the position is completely unknown. In general, and Heisenberg's Uncertainty Principles W. Heisenberg in 1927 If,then,, and.
9 Uncertainty Principle The velocity of an electronmoving along x-axis = 2.05x10 6 m/s.and the uncertainty is 0.50 %. What is the minimum uncertainty when the position is measured simultaneously? =(9.11x10-31 )(2.05x10 6 ) = 1.87x10-24 kgㆍm/s = (0.0050)(1.87x10-24 ) = 9.35x10-27 kgㆍm/s = 1.13x10-8 m = 11.3 nm
10 Potential step 1 incoming wave 1. At, 2.1For,at with Thewavemusttravel in direction
11 Properties of the wavefunctions 1. The wavefunction should be continuous 2. The first derivative of the wavefunction should be continuous Namely,at theinterface( ) and
12 Potentialstep 2(for ) Soat Reflection: and : even, non-zeroprob. ofturning back! (optical analogy) :theparticlewill bereflectedortransmitted Transmission: goes1as
13 Potential step 3 2.2For,at with Thewavefunction shoulddecay inthebarrier At and
14 Potentialstep 4 (for ) Reflection As in C.M., the particle is always reflected(total reflection). But non-zero prob.( ) ofpresenceintheclassically forbidden region!! iscomplex:phaseshift upon reflection
15 Potential barrier 1 For 1)for : 2)for : 3)for : with and At, at,
16 Potentialbarrier2(for ) and again! :oscillates!! when (i.e. ), : resonance
17 Transmission Probability ev, nm ev, nm
18 Potentialbarrier3(for ) for for (for ) for with and
19 Potentialbarrier4(for ) Byreplacing in theaboveresultswith when, and where Non-zero prob. of crossing the potential barrier: tunneling
20 Tunneling Probability In general, the transmission probability is given by where and arethe2classical turning points for the potential barrier.
21 Tunneling alpha-decay scanning tunneling microscope(stm) As tip is scanned laterally across the surface, thetipis moved up or down to keep the tunneling current(tip to surface distance ) constant. Asaresult, thetip maps outthecontoursofthesurfacewith resolutiononthescaleof1nminstead of >300 nm for optical microscopes! 92U Th He ++ () From the tunneling prob., the lifetime can be estimated.
22 STM images Blue Platinum Quantum Corral Pt(111) Iron on Copper(111)
23 Tunneling Probability Anelectron with = 5.1 ev approaches to asquare barrier with the height of 6.8 ev and the thickness of 750 pm. What is the probability to find the electron tunneling through? where = 6.67x10 9 m -1 = 10.0 =4.5x10-5. The energy of the electronpassing through=5.1 ev What is the probability for a protonwith =5.1 ev? : mathematically not the same as 0 but practically almost same as 0
Final Exam: Tuesday, May 8, 2012 Starting at 8:30 a.m., Hoyt Hall.
Final Exam: Tuesday, May 8, 2012 Starting at 8:30 a.m., Hoyt Hall. Chapter 38 Quantum Mechanics Units of Chapter 38 38-1 Quantum Mechanics A New Theory 37-2 The Wave Function and Its Interpretation; the
More information* = 2 = Probability distribution function. probability of finding a particle near a given point x,y,z at a time t
Quantum Mechanics Wave functions and the Schrodinger equation Particles behave like waves, so they can be described with a wave function (x,y,z,t) A stationary state has a definite energy, and can be written
More informationQUANTUM PHYSICS II. Challenging MCQ questions by The Physics Cafe. Compiled and selected by The Physics Cafe
QUANTUM PHYSICS II Challenging MCQ questions by The Physics Cafe Compiled and selected by The Physics Cafe 1 Suppose Fuzzy, a quantum-mechanical duck of mass 2.00 kg, lives in a world in which h, the Planck
More informationPHY 114 A General Physics II 11 AM-12:15 PM TR Olin 101
PHY 114 A General Physics II 11 AM-1:15 PM TR Olin 101 Plan for Lecture 3 (Chapter 40-4): Some topics in Quantum Theory 1. Particle behaviors of electromagnetic waves. Wave behaviors of particles 3. Quantized
More information4/14/2015. Models of the Atom. Quantum Physics versus Classical Physics The Thirty-Year War ( ) Classical Model of Atom
Quantum Physics versus Classical Physics The Thirty-Year War (1900-1930) Models of the Atom Interactions between Matter and Radiation Models of the Atom Bohr s Model of the Atom Planck s Blackbody Radiation
More informationCOLLEGE PHYSICS. Chapter 30 ATOMIC PHYSICS
COLLEGE PHYSICS Chapter 30 ATOMIC PHYSICS Matter Waves: The de Broglie Hypothesis The momentum of a photon is given by: The de Broglie hypothesis is that particles also have wavelengths, given by: Matter
More informationChapter 28 Quantum Theory Lecture 24
Chapter 28 Quantum Theory Lecture 24 28.1 Particles, Waves, and Particles-Waves 28.2 Photons 28.3 Wavelike Properties Classical Particles 28.4 Electron Spin 28.5 Meaning of the Wave Function 28.6 Tunneling
More informationChapter 38. Photons and Matter Waves
Chapter 38 Photons and Matter Waves The sub-atomic world behaves very differently from the world of our ordinary experiences. Quantum physics deals with this strange world and has successfully answered
More informationLecture Outline Chapter 30. Physics, 4 th Edition James S. Walker. Copyright 2010 Pearson Education, Inc.
Lecture Outline Chapter 30 Physics, 4 th Edition James S. Walker Chapter 30 Quantum Physics Units of Chapter 30 Blackbody Radiation and Planck s Hypothesis of Quantized Energy Photons and the Photoelectric
More information3.23 Electrical, Optical, and Magnetic Properties of Materials
MIT OpenCourseWare http://ocw.mit.edu 3.23 Electrical, Optical, and Magnetic Properties of Materials Fall 2007 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.
More informationQuantum Mysteries. Scott N. Walck. September 2, 2018
Quantum Mysteries Scott N. Walck September 2, 2018 Key events in the development of Quantum Theory 1900 Planck proposes quanta of light 1905 Einstein explains photoelectric effect 1913 Bohr suggests special
More informationQuantum Mechanics. The Schrödinger equation. Erwin Schrödinger
Quantum Mechanics The Schrödinger equation Erwin Schrödinger The Nobel Prize in Physics 1933 "for the discovery of new productive forms of atomic theory" The Schrödinger Equation in One Dimension Time-Independent
More informationDEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS
DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS TSOKOS LESSON 1-1B: THE INTERACTION OF MATTER WITH RADIATION Introductory Video Quantum Mechanics Essential Idea: The microscopic quantum world offers
More informationChap. 3. Elementary Quantum Physics
Chap. 3. Elementary Quantum Physics 3.1 Photons - Light: e.m "waves" - interference, diffraction, refraction, reflection with y E y Velocity = c Direction of Propagation z B z Fig. 3.1: The classical view
More information12/04/2012. Models of the Atom. Quantum Physics versus Classical Physics The Thirty-Year War ( )
Quantum Physics versus Classical Physics The Thirty-Year War (1900-1930) Interactions between Matter and Radiation Models of the Atom Bohr s Model of the Atom Planck s Blackbody Radiation Models of the
More informationQuantum Mechanical Tunneling
The square barrier: Quantum Mechanical Tunneling Behaviour of a classical ball rolling towards a hill (potential barrier): If the ball has energy E less than the potential energy barrier (U=mgy), then
More informationMatter Waves. Chapter 5
Matter Waves Chapter 5 De Broglie pilot waves Electromagnetic waves are associated with quanta - particles called photons. Turning this fact on its head, Louis de Broglie guessed : Matter particles have
More informationWhich of the following can be used to calculate the resistive force acting on the brick? D (Total for Question = 1 mark)
1 A brick of mass 5.0 kg falls through water with an acceleration of 0.90 m s 2. Which of the following can be used to calculate the resistive force acting on the brick? A 5.0 (0.90 9.81) B 5.0 (0.90 +
More informationtip conducting surface
PhysicsAndMathsTutor.com 1 1. The diagram shows the tip of a scanning tunnelling microscope (STM) above a conducting surface. The tip is at a potential of 1.0 V relative to the surface. If the tip is sufficiently
More informationModule 40: Tunneling Lecture 40: Step potentials
Module 40: Tunneling Lecture 40: Step potentials V E I II III 0 x a Figure 40.1: A particle of energy E is incident on a step potential of hight V > E as shown in Figure 40.1. The step potential extends
More informationChapter 8 Chapter 8 Quantum Theory: Techniques and Applications (Part II)
Chapter 8 Chapter 8 Quantum Theory: Techniques and Applications (Part II) The Particle in the Box and the Real World, Phys. Chem. nd Ed. T. Engel, P. Reid (Ch.16) Objectives Importance of the concept for
More informationCHAPTER 6 Quantum Mechanics II
CHAPTER 6 Quantum Mechanics II 6.1 The Schrödinger Wave Equation 6.2 Expectation Values 6.3 Infinite Square-Well Potential 6.4 Finite Square-Well Potential 6.5 Three-Dimensional Infinite-Potential Well
More informationParticles and Waves Particles Waves
Particles and Waves Particles Discrete and occupy space Exist in only one location at a time Position and velocity can be determined with infinite accuracy Interact by collisions, scattering. Waves Extended,
More informationClass 21. Early Quantum Mechanics and the Wave Nature of Matter. Physics 106. Winter Press CTRL-L to view as a slide show. Class 21.
Early and the Wave Nature of Matter Winter 2018 Press CTRL-L to view as a slide show. Last Time Last time we discussed: Optical systems Midterm 2 Today we will discuss: Quick of X-ray diffraction Compton
More informationLecture 16 Quantum Physics Chapter 28
Lecture 16 Quantum Physics Chapter 28 Particles vs. Waves Physics of particles p = mv K = ½ mv2 Particles collide and do not pass through each other Conservation of: Momentum Energy Electric Charge Physics
More informationProbability and Normalization
Probability and Normalization Although we don t know exactly where the particle might be inside the box, we know that it has to be in the box. This means that, ψ ( x) dx = 1 (normalization condition) L
More informationQuantum Theory. Thornton and Rex, Ch. 6
Quantum Theory Thornton and Rex, Ch. 6 Matter can behave like waves. 1) What is the wave equation? 2) How do we interpret the wave function y(x,t)? Light Waves Plane wave: y(x,t) = A cos(kx-wt) wave (w,k)
More informationPHYS 571 Radiation Physics
PHYS 571 Radiation Physics Prof. Gocha Khelashvili http://blackboard.iit.edu login Bohr s Theory of Hydrogen Atom Bohr s Theory of Hydrogen Atom Bohr s Theory of Hydrogen Atom Electrons can move on certain
More informationChapter 10: Wave Properties of Particles
Chapter 10: Wave Properties of Particles Particles such as electrons may demonstrate wave properties under certain conditions. The electron microscope uses these properties to produce magnified images
More informationCHAPTER 6 Quantum Mechanics II
CHAPTER 6 Quantum Mechanics II 6.1 6.2 6.3 6.4 6.5 6.6 6.7 The Schrödinger Wave Equation Expectation Values Infinite Square-Well Potential Finite Square-Well Potential Three-Dimensional Infinite-Potential
More informationThe Schrödinger Equation in One Dimension
The Schrödinger Equation in One Dimension Introduction We have defined a comple wave function Ψ(, t) for a particle and interpreted it such that Ψ ( r, t d gives the probability that the particle is at
More informationElectron in a Box. A wave packet in a square well (an electron in a box) changing with time.
Electron in a Box A wave packet in a square well (an electron in a box) changing with time. Last Time: Light Wave model: Interference pattern is in terms of wave intensity Photon model: Interference in
More informationDynamics inertia, mass, force. Including centripetal acceleration
For the Singapore Junior Physics Olympiad, no question set will require the use of calculus. However, solutions of questions involving calculus are acceptable. 1. Mechanics Kinematics position, displacement,
More informationInterpretations of Quantum Mechanics. Quantum Weirdness Part 4. The Copenhagen Interpretation. Correspondence Principle. Who Invented the Term?
Quantum Weirdness Part 4 Interpretations of Quantum Mechanics What does it mean? The Uncertainty Principle Interpretations Of Quantum Mechanics Quantum Tunnelling The Copenhagen Interpretation A wavefunction
More informationPHYS 4 CONCEPT PACKET Complete
PHYS 4 CONCEPT PACKET Complete Written by Jeremy Robinson, Head Instructor Find Out More +Private Instruction +Review Sessions WWW.GRADEPEAK.COM Need Help? Online Private Instruction Anytime, Anywhere
More informationU(x) Finite Well. E Re ψ(x) Classically forbidden
Final Exam Physics 2130 Modern Physics Tuesday December 18, 2001 Point distribution: All questions are worth points 8 points. Answers should be bubbled onto the answer sheet. 1. At what common energy E
More informationESSEX COUNTY COLLEGE Mathematics and Physics Division PHY 203 General Physics III Course Outline
ESSEX COUNTY COLLEGE Mathematics and Physics Division PHY 203 General Physics III Course Outline Course Number & Name: PHY 203 General Physics III Credit Hours: 5.0 Contact Hours: 7.0 Lecture/Lab: 7.0
More informationQuantum Theory and the Electronic Structure of Atoms
Quantum Theory and the Electronic Structure of Atoms Chapter 7 Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1 Properties of Waves Wavelength ( ) is the distance
More informationDEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS
DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS LSN 12-1A: INTERACTIONS OF MATTER WITH RADIATION Questions From Reading Activity? Essential Idea: The microscopic quantum world offers a range of phenomena,
More informationParticle in a box. From Last Time. Classical vs quantum. Wavefunction of pendulum. Wavefunctions in two dimensions. Probability density of oscillator
No office hours Tuesday Guest lecturer Wed: Entanglement & Quantum Computing From ast Time Particle can exist in different quantum states, having Different energy Different momentum Different wavelength
More informationGeneral Physics (PHY 2140) Lecture 15
General Physics (PHY 2140) Lecture 15 Modern Physics Chapter 27 1. Quantum Physics The Compton Effect Photons and EM Waves Wave Properties of Particles Wave Functions The Uncertainty Principle http://www.physics.wayne.edu/~alan/2140website/main.htm
More informationSupplemental Activities. Module: Atomic Theory. Section: Electromagnetic Radiation and Matter
Supplemental Activities Module: Atomic Theory Section: Electromagnetic Radiation and Matter Introduction to Electromagnetic Radiation Activity 1 1. What are the two components that make up electromagnetic
More informationDavid J. Starling Penn State Hazleton PHYS 214
All the fifty years of conscious brooding have brought me no closer to answer the question, What are light quanta? Of course today every rascal thinks he knows the answer, but he is deluding himself. -Albert
More informationFundamental of Spectroscopy for Optical Remote Sensing Xinzhao Chu I 10 3.4. Principle of Uncertainty Indeterminacy 0. Expression of Heisenberg s Principle of Uncertainty It is worth to point out that
More informationThe Structure of the Atom Review
The Structure of the Atom Review Atoms are composed of PROTONS + positively charged mass = 1.6726 x 10 27 kg NEUTRONS neutral mass = 1.6750 x 10 27 kg ELECTRONS negatively charged mass = 9.1096 x 10 31
More informationWave function and Quantum Physics
Wave function and Quantum Physics Properties of matter Consists of discreet particles Atoms, Molecules etc. Matter has momentum (mass) A well defined trajectory Does not diffract or interfere 1 particle
More informationThere is light at the end of the tunnel. -- proverb. The light at the end of the tunnel is just the light of an oncoming train. --R.
A vast time bubble has been projected into the future to the precise moment of the end of the universe. This is, of course, impossible. --D. Adams, The Hitchhiker s Guide to the Galaxy There is light at
More informationThe wavefunction ψ for an electron confined to move within a box of linear size L = m, is a standing wave as shown.
1. This question is about quantum aspects of the electron. The wavefunction ψ for an electron confined to move within a box of linear size L = 1.0 10 10 m, is a standing wave as shown. State what is meant
More informationBohr s Correspondence Principle
Bohr s Correspondence Principle In limit that n, quantum mechanics must agree with classical physics E photon = 13.6 ev 1 n f n 1 i = hf photon In this limit, n i n f, and then f photon electron s frequency
More informationLarbert High School. Quanta and Waves. Homework Exercises ADVANCED HIGHER PHYSICS
Larbert High School ADVANCED HIGHER PHYSICS Quanta and Waves Homework Exercises 3.1 3.6 3.1 Intro to Quantum Theory HW 1. (a) Explain what is meant by term black body. (1) (b) State two observations that
More informationCHAPTER 6 Quantum Mechanics II
CHAPTER 6 Quantum Mechanics II 6.1 The Schrödinger Wave Equation 6.2 Expectation Values 6.3 Infinite Square-Well Potential 6.4 Finite Square-Well Potential 6.5 Three-Dimensional Infinite-Potential Well
More informationEcole Franco-Roumaine : Magnétisme des systèmes nanoscopiques et structures hybrides - Brasov, Modern Analytical Microscopic Tools
1. Introduction Solid Surfaces Analysis Group, Institute of Physics, Chemnitz University of Technology, Germany 2. Limitations of Conventional Optical Microscopy 3. Electron Microscopies Transmission Electron
More informationChapter 37 Early Quantum Theory and Models of the Atom. Copyright 2009 Pearson Education, Inc.
Chapter 37 Early Quantum Theory and Models of the Atom Planck s Quantum Hypothesis; Blackbody Radiation Photon Theory of Light and the Photoelectric Effect Energy, Mass, and Momentum of a Photon Compton
More informationPhysics 126 Practice Exam #4 Professor Siegel
Physics 126 Practice Exam #4 Professor Siegel Name: Lab Day: 1. Light is usually thought of as wave-like in nature and electrons as particle-like. In which one of the following instances does light behave
More informationCHAPTER 2: POSTULATES OF QUANTUM MECHANICS
CHAPTER 2: POSTULATES OF QUANTUM MECHANICS Basics of Quantum Mechanics - Why Quantum Physics? - Classical mechanics (Newton's mechanics) and Maxwell's equations (electromagnetics theory) can explain MACROSCOPIC
More informationExercise 1 Atomic line spectra 1/9
Exercise 1 Atomic line spectra 1/9 The energy-level scheme for the hypothetical one-electron element Juliettium is shown in the figure on the left. The potential energy is taken to be zero for an electron
More informationPHY202 Quantum Mechanics. Topic 1. Introduction to Quantum Physics
PHY202 Quantum Mechanics Topic 1 Introduction to Quantum Physics Outline of Topic 1 1. Dark clouds over classical physics 2. Brief chronology of quantum mechanics 3. Black body radiation 4. The photoelectric
More informationSemiconductor Physics and Devices
Introduction to Quantum Mechanics In order to understand the current-voltage characteristics, we need some knowledge of electron behavior in semiconductor when the electron is subjected to various potential
More informationUnbound States. 6.3 Quantum Tunneling Examples Alpha Decay The Tunnel Diode SQUIDS Field Emission The Scanning Tunneling Microscope
Unbound States 6.3 Quantum Tunneling Examples Alpha Decay The Tunnel Diode SQUIDS Field Emission The Scanning Tunneling Microscope 6.4 Particle-Wave Propagation Phase and Group Velocities Particle-like
More informationQuantum Theory. Thornton and Rex, Ch. 6
Quantum Theory Thornton and Rex, Ch. 6 Matter can behave like waves. 1) What is the wave equation? 2) How do we interpret the wave function y(x,t)? Light Waves Plane wave: y(x,t) = A cos(kx-wt) wave (w,k)
More information5.111 Principles of Chemical Science
MIT OpenCourseWare http://ocw.mit.edu 5.111 Principles of Chemical Science Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. 5.111 Lecture Summary
More informationUnit title: Atomic and Nuclear Physics for Spectroscopic Applications
Unit title: Atomic and Nuclear Physics for Spectroscopic Applications Unit code: Y/601/0417 QCF level: 4 Credit value: 15 Aim This unit provides an understanding of the underlying atomic and nuclear physics
More informationPHYS 3313 Section 001 Lecture # 22
PHYS 3313 Section 001 Lecture # 22 Dr. Barry Spurlock Simple Harmonic Oscillator Barriers and Tunneling Alpha Particle Decay Schrodinger Equation on Hydrogen Atom Solutions for Schrodinger Equation for
More informationOne-dimensional potentials: potential step
One-dimensional potentials: potential step Figure I: Potential step of height V 0. The particle is incident from the left with energy E. We analyze a time independent situation where a current of particles
More informationEE 4395 Special Topics Applied Quantum Mechanics for Electrical Engineers Homework Problems
EE 4395 Special Topics Applied Quantum Mechanics for Electrical Engineers Homework Problems Part II: Electromagnetic Waves 2.1 Use the relativistic formulas for total energy (γmc 2 )and momentum (γmv)
More informationDept. of Physics, MIT Manipal 1
Chapter 1: Optics 1. In the phenomenon of interference, there is A Annihilation of light energy B Addition of energy C Redistribution energy D Creation of energy 2. Interference fringes are obtained using
More informationCh 7 Quantum Theory of the Atom (light and atomic structure)
Ch 7 Quantum Theory of the Atom (light and atomic structure) Electromagnetic Radiation - Electromagnetic radiation consists of oscillations in electric and magnetic fields. The oscillations can be described
More informationMIDTERM 3 REVIEW SESSION. Dr. Flera Rizatdinova
MIDTERM 3 REVIEW SESSION Dr. Flera Rizatdinova Summary of Chapter 23 Index of refraction: Angle of reflection equals angle of incidence Plane mirror: image is virtual, upright, and the same size as the
More informationVICTORIA JUNIOR COLLEGE 2014 JC2 PRELIMINARY EXAMINATION. 23/9/ h 1600h
Name: Class: 13S VICTORIA JUNIOR COLLEGE 2014 JC2 PRELIMINARY EXAMINATION PHYSICS 9646/3 Higher 2 Paper 3 23/9/2014 1400h 1600h TUESDAY (2 Hours) This paper consists of two sections: Section A (40 marks)
More informationModern Physics for Scientists and Engineers International Edition, 4th Edition
Modern Physics for Scientists and Engineers International Edition, 4th Edition http://optics.hanyang.ac.kr/~shsong Review: 1. THE BIRTH OF MODERN PHYSICS 2. SPECIAL THEORY OF RELATIVITY 3. THE EXPERIMENTAL
More informationSemiconductor Physics and Devices
EE321 Fall 2015 September 28, 2015 Semiconductor Physics and Devices Weiwen Zou ( 邹卫文 ) Ph.D., Associate Prof. State Key Lab of advanced optical communication systems and networks, Dept. of Electronic
More informationOpinions on quantum mechanics. CHAPTER 6 Quantum Mechanics II. 6.1: The Schrödinger Wave Equation. Normalization and Probability
CHAPTER 6 Quantum Mechanics II 6.1 The Schrödinger Wave Equation 6. Expectation Values 6.3 Infinite Square-Well Potential 6.4 Finite Square-Well Potential 6.5 Three-Dimensional Infinite- 6.6 Simple Harmonic
More informationElectronic Structure of Atoms. Chapter 6
Electronic Structure of Atoms Chapter 6 Electronic Structure of Atoms 1. The Wave Nature of Light All waves have: a) characteristic wavelength, λ b) amplitude, A Electronic Structure of Atoms 1. The Wave
More informationFinal Exam. Tuesday, May 8, Starting at 8:30 a.m., Hoyt Hall.
Final Exam Tuesday, May 8, 2012 Starting at 8:30 a.m., Hoyt Hall. Summary of Chapter 38 In Quantum Mechanics particles are represented by wave functions Ψ. The absolute square of the wave function Ψ 2
More information... State what is meant by ionisation energy. ...
Q1.Sodium metal has a work function of 2.28 ev. An atom of sodium has an ionisation energy of 5.15 ev. (a) (i) State what is meant by work function. (ii) State what is meant by ionisation energy. (b) Show
More informationNuclear Binding Energy
Nuclear Energy Nuclei contain Z number of protons and (A - Z) number of neutrons, with A the number of nucleons (mass number) Isotopes have a common Z and different A The masses of the nucleons and the
More informationLecture 15 Notes: 07 / 26. The photoelectric effect and the particle nature of light
Lecture 15 Notes: 07 / 26 The photoelectric effect and the particle nature of light When diffraction of light was discovered, it was assumed that light was purely a wave phenomenon, since waves, but not
More informationPlanck s Quantum Hypothesis Blackbody Radiation
Planck s Quantum Hypothesis Blackbody Radiation The spectrum of blackbody radiation has been measured(next slide); it is found that the frequency of peak intensity increases linearly with temperature.
More informationCHAPTER 6 Quantum Mechanics II
CHAPTER 6 Quantum Mechanics II 6.1 The Schrödinger Wave Equation 6.2 Expectation Values 6.3 Infinite Square-Well Potential 6.4 Finite Square-Well Potential 6.5 Three-Dimensional Infinite-Potential Well
More informationLecture 13: Barrier Penetration and Tunneling
Lecture 13: Barrier Penetration and Tunneling nucleus x U(x) U(x) U 0 E A B C B A 0 L x 0 x Lecture 13, p 1 Today Tunneling of quantum particles Scanning Tunneling Microscope (STM) Nuclear Decay Solar
More informationLecture 4 Introduction to Quantum Mechanical Way of Thinking.
Lecture 4 Introduction to Quantum Mechanical Way of Thinking. Today s Program 1. Brief history of quantum mechanics (QM). 2. Wavefunctions in QM (First postulate) 3. Schrodinger s Equation Questions you
More informationChapter 30 Quantum Physics 30.1 Blackbody Radiation and Planck s Hypothesis of Quantum Energy 30.2 Photons and the Photoelectric Effect 30.
Chapter 30 Quantum Physics 30.1 Blackbody Radiation and Planck s Hypothesis of Quantum Energy 30.2 Photons and the Photoelectric Effect 30.3 The Mass and Momentum of a Photon 30.4 Photon Scattering and
More informationLecture 36 Chapter 31 Light Quanta Matter Waves Uncertainty Principle
Lecture 36 Chapter 31 Light Quanta Matter Waves Uncertainty Principle 24-Nov-10 Birth of Quantum Theory There has been a long historical debate about the nature of light: Some believed it to be particle-like.
More informationQuantum Physics Lecture 9
Quantum Physics Lecture 9 Potential barriers and tunnelling Examples E < U o Scanning Tunelling Microscope E > U o Ramsauer-Townsend Effect Angular Momentum - Orbital - Spin Pauli exclusion principle potential
More informationChapter 37 Early Quantum Theory and Models of the Atom
Chapter 37 Early Quantum Theory and Models of the Atom Units of Chapter 37 37-7 Wave Nature of Matter 37-8 Electron Microscopes 37-9 Early Models of the Atom 37-10 Atomic Spectra: Key to the Structure
More informationPHYS 3313 Section 001 Lecture #16
PHYS 3313 Section 001 Lecture #16 Monday, Mar. 24, 2014 De Broglie Waves Bohr s Quantization Conditions Electron Scattering Wave Packets and Packet Envelops Superposition of Waves Electron Double Slit
More informationSummary of Last Time Barrier Potential/Tunneling Case I: E<V 0 Describes alpha-decay (Details are in the lecture note; go over it yourself!!) Case II:
Quantum Mechanics and Atomic Physics Lecture 8: Scattering & Operators and Expectation Values http://www.physics.rutgers.edu/ugrad/361 Prof. Sean Oh Summary of Last Time Barrier Potential/Tunneling Case
More informationCHAPTER 28 Quantum Mechanics of Atoms Units
CHAPTER 28 Quantum Mechanics of Atoms Units Quantum Mechanics A New Theory The Wave Function and Its Interpretation; the Double-Slit Experiment The Heisenberg Uncertainty Principle Philosophic Implications;
More informationQUANTUM MECHANICS Intro to Basic Features
PCES 4.21 QUANTUM MECHANICS Intro to Basic Features 1. QUANTUM INTERFERENCE & QUANTUM PATHS Rather than explain the rules of quantum mechanics as they were devised, we first look at a more modern formulation
More informationHydrogen atom energies. Friday Honors lecture. Quantum Particle in a box. Classical vs Quantum. Quantum version
Friday onors lecture Prof. Clint Sprott takes us on a tour of fractals. ydrogen atom energies Quantized energy levels: Each corresponds to different Orbit radius Velocity Particle wavefunction Energy Each
More informationWe also find the development of famous Schrodinger equation to describe the quantization of energy levels of atoms.
Lecture 4 TITLE: Quantization of radiation and matter: Wave-Particle duality Objectives In this lecture, we will discuss the development of quantization of matter and light. We will understand the need
More informationPhysics 111 Homework Solutions Week #9 - Thursday
Physics 111 Homework Solutions Week #9 - Thursday Monday, March 1, 2010 Chapter 24 241 Based on special relativity we know that as a particle with mass travels near the speed of light its mass increases
More informationPhysics 217 Problem Set 1 Due: Friday, Aug 29th, 2008
Problem Set 1 Due: Friday, Aug 29th, 2008 Course page: http://www.physics.wustl.edu/~alford/p217/ Review of complex numbers. See appendix K of the textbook. 1. Consider complex numbers z = 1.5 + 0.5i and
More informationWavelength of 1 ev electron
HW8: M Chap 15: Question B, Exercises 2, 6 M Chap 16: Question B, Exercises 1 M Chap 17: Questions C, D From Last Time Essay topic and paragraph due Friday, Mar. 24 Light waves are particles and matter
More informationSupplemental Activities. Module: Atomic Theory. Section: Electromagnetic Radiation and Matter - Key
Supplemental Activities Module: Atomic Theory Section: Electromagnetic Radiation and Matter - Key Introduction to Electromagnetic Radiation Activity 1 1. What are the two components that make up electromagnetic
More informationQuantum Theory of the Atom
Quantum Theory of the Atom The Wave Nature of Light A wave is a continuously repeating change or oscillation in matter or in a physical field. Light is also a wave. It consists of oscillations in electric
More informationStudents are required to pass a minimum of 15 AU of PAP courses including the following courses:
School of Physical and Mathematical Sciences Division of Physics and Applied Physics Minor in Physics Curriculum - Minor in Physics Requirements for the Minor: Students are required to pass a minimum of
More informationPHY100/Exam2 Page 2 of 5 Name: (12 pts )
PHY100 November 12, 2008 Exam 2 Name: Aran Garcia-Bellido Please read the problems carefully and answer them in the space provided. Write on the back of the page, if necessary. Show your work where requested
More informationPhysics 107 Final Exam December 13, Your Name: Questions
Physics 107 Final Exam December 13, 1993 Your Name: Questions 1. 11. 21. 31. 41. 2. 12. 22. 32. 42. 3. 13. 23. 33. 43. 4. 14. 24. 34. 44. 5. 15. 25. 35. 45. 6. 16. 26. 36. 46. 7. 17. 27. 37. 47. 8. 18.
More informationLasers. Stimulated Emission Lasers: Trapping Photons Terahertz Lasers Course Overview
Lasers Stimulated Emission Lasers: Trapping Photons Terahertz Lasers Course Overview 1 P-N Junctions and LEDs Terminal Pins Emitted Light Beams Diode Transparent Plastic Case High energy electrons (n-type)
More information