From Atoms to Materials: Predictive Theory and Simulations. Materials are everywhere
|
|
- Albert Haynes
- 5 years ago
- Views:
Transcription
1 Fom Atoms to Mateials: Pedictive Theoy and Simulations Intoduction Ale Stachan School of Mateials Engineeing & Bick Nanotechnology Cente Pudue Univesity West Lafayette, Indiana USA Mateials ae eveywhee Stuctual mateials Phamaceuticals Kwong, Kauffman, Hute & Muelle Natue Biotechnology, 9, 993 (011) Nanoelectonics The High-k Solution, Boh, Chau, Ghani, and Misty Ale Stachan Atoms to Mateials 1
2 Leaning objectives In Atoms to Mateials you will: Lean the basics physics that goven mateials at atomic scales Relate these pocesses to the macoscopic wold Use online to enhance leaning Density theoy Molecula dynamics Ale Stachan Atoms to Mateials 3 Mateials at molecula scales Molecula mateials Ceamics & semiconductos Metals Ale Stachan Atoms to Mateials 4
3 Mateials popeties Mateials Selection in Mechanical Design (3d edition) by MF Ashby, Buttewoth Heinemann, 005 Ale Stachan Atoms to Mateials 5 Pedictive science of mateials The fundamental laws necessay fo the mathematical teatment of a lage pat of physics and the whole of chemisty ae thus completely known, and the difficulty lies only in the fact that application of these laws leads to equations that ae too complex to be solved. Ale Stachan Atoms to Mateials 6 3
4 Fundamental physics & appoximations Quantum mechanics: A goup of atoms can be fully descibed by thei wavefunction The time evolution of this wavefunction is given by the Schödinge equation i d dt Ψ,t ( ) = HΨ (,t ) Too complex to be solved even with supecomputes Electons: Time independent Schödinge Eq. Ions: Classical (Newton s) mechanics Hψ = Eψ F = ma Ale Stachan Atoms to Mateials 7 Electonic and atomic pocesses Initial condition { } { R i } V i Time evolution R i = V i V i = F i M i Enegy & foces Hψ = Eψ F i = Ri E ({ R i }) Ale Stachan Atoms to Mateials 8 4
5 Molecula dynamics Initial conditions { R i } V i { } Compute enegy & foces Hψ = Eψ F i = Ri E ({ R i }) Integate Eqs. of Motion R i V i ( t) R i ( t + Δt) ( t) V i ( t + Δt) Ale Stachan Atoms to Mateials 9 Micoscopic and macoscopic wolds Ale Stachan Atoms to Mateials 10 5
6 Couse outline The quantum mechanics of bonding and electonic stuctue Atoms, molecules and cystals Electonic stuctue calculations Hatee-Fock & post-hatee-fock methods Density functional theoy Beyond density functional theoy Popety pedictions Classical and statistical mechanics Hamilton s fomalism of classical mechanics Nomal modes and phonons Statistical mechanics (classical, Bose-Einstein, and Femi-Diac) Molecula dynamics simulations Inteatomic potentials fo vaious classes of mateials Computing the themo-mechanical esponse of mateials Kinetic theoy and Boltzmann equation Dynamics with Implicit Degees of Feedom Coase gained simulations of molecula mateials Two tempeatue model and electonic themal tanspot Atomistic simulations Ale Stachan of electochemical Atoms to Mateials eactions 11 Gading policy Gading Policy Poject Repot: 40% Quizzes: 0% Final Exam (take home): 40% Ale Stachan Atoms to Mateials 1 6
7 Couse esouces Couse webpage: hops://nanohub.og/couses/mse697 Couse nanohub goup: hops://nanohub.og/goups/atomsmateials Books fo Pat 1 electonic stuctue The natue of the chemical bond, William A. Goddad, III hop://authos.libay.caltech.edu/50/ Quantum Mechanics, Claude Cohen- Tannoudji, Benad Diu, Fank Laloe Atoms and Molecules: An Intoduc8on fo Students of Physical Chemisty, M. Kaplus, Richad Needham Pote Electonic Stuctue and the Pope@es of Solids, Walte A. Haison Computa6onal Physics - J. M. Thijssen Ale Stachan Atoms to Mateials 13 Fom Atoms to Mateials: Pedictive Theoy and Simulations Why Quantum Mechanics? Ale Stachan stachan@pudue.edu School of Mateials Engineeing & Bick Nanotechnology Cente Pudue Univesity West Lafayette, Indiana USA 7
8 The simplest atom: hydogen What if we teat it with classical mechanics? Poton (e) State of the system (assume massive poton is fixed in space) Position and velocity of electon t ( ) υ t ( ) Enegy (equilibium will coespond to minimum enegy) Electon (- e) Potential: V (! ) = Potential enegy distance Linea momentum Kinetic Enegy: K = 1 m v p = m Alejando Stachan Atoms to Mateials 1 Classical Hydogen poton Electon (e - ) What if we teat it with classical mechanics? Enegy: E = e + p m State with minimum enegy (equilibium)? Alejando Stachan Atoms to Mateials 8
9 Ty Quantum Mechanics poton Electon (- e) State of the system wave function (a function of position () that descibes the pobability of finding the electon at position ) ψ ψ ( ) Physical Obsevable opeato (a mathematical object that acts on a function) Χ Position: Mul@ply by Momentum:! p =!! i Gadient Alejando Stachan Atoms to Mateials 4 Quantum mechanics poton Electon (e - ) Expeimental measuements: expectation value of an opeato Integal ove all space: Example:! = O = ψ ( )Oψ ( )dx dy dz Integal ove all space dx. dy dz WF squaed is the pobability density of finding the electon aound posi@on 3 d Alejando Stachan Atoms to Mateials 5 9
10 Quantum hydogen poton Electon (e - ) H = $ Ψ & % ( ) m e ' )Ψ( )d 3 ( = m ( ) Ψ ( ) Ψ Ψ( )d 3 e d 3 To minimize the enegy: Kinetic enegy: Potential enegy: Alejando Stachan Atoms to Mateials 6 Quantum hydogen poton Electon (-e) ( ) H = m Ψ ( ) Ψ Ψ( )d 3 e d 3 WF WF WF x Potential Potential Potential Alejando Stachan Atoms to Mateials 7 10
11 Summay Classical mechanics State of the system:!! ( t) p( t) Enegy: qiq j e V = = p 1 K = = mv m Gound state (minimum enegy): = 0 E = Atoms do not exist!! poton Electon (e - ) Classical mechanics fails: quantum mechanics State: wave function: ( ) E =! Enegy: m! ψ e Gound state: finite size The kinetic enegy makes atoms stable Alejando Stachan Atoms to Mateials 8 11
DENSITY-FUNCTIONAL THEORY, AND DENSITY-FUNCTIONAL PRACTICE
3.320: Lectue 7 Feb 24 2005 DENSITY-FUNCTIONAL THEORY, AND DENSITY-FUNCTIONAL PRACTICE Feb 24 2005 3.320 Atomistic Modeling of Mateials -- Geband Cede and Nicola Mazai Hatee-Fock Equations ψ,,..., = 1
More informationTeoría del Funcional de la Densidad (Density Functional Theory)
Teoía del Funcional de la Densidad (Density Functional Theoy) Motivation: limitations of the standad appoach based on the wave function. The electonic density n() as the key vaiable: Functionals & Thomas-Femi
More informationA Hartree-Fock Example Using Helium
Univesity of Connecticut DigitalCommons@UConn Chemisty Education Mateials Depatment of Chemisty June 6 A Hatee-Fock Example Using Helium Cal W. David Univesity of Connecticut, Cal.David@uconn.edu Follow
More information20th Century Atomic Theory - Hydrogen Atom
0th Centuy Atomic Theoy - Hydogen Atom Ruthefod s scatteing expeiments (Section.5, pp. 53-55) in 1910 led to a nuclea model of the atom whee all the positive chage and most of the mass wee concentated
More informationLecture 7: Angular Momentum, Hydrogen Atom
Lectue 7: Angula Momentum, Hydogen Atom Vecto Quantization of Angula Momentum and Nomalization of 3D Rigid Roto wavefunctions Conside l, so L 2 2 2. Thus, we have L 2. Thee ae thee possibilities fo L z
More informationb Ψ Ψ Principles of Organic Chemistry lecture 22, page 1
Pinciples of Oganic Chemisty lectue, page. Basis fo LCAO and Hückel MO Theoy.. Souces... Hypephysics online. http://hypephysics.phy-ast.gsu.edu/hbase/quantum/qm.html#c... Zimmeman, H. E., Quantum Mechanics
More information11) A thin, uniform rod of mass M is supported by two vertical strings, as shown below.
Fall 2007 Qualifie Pat II 12 minute questions 11) A thin, unifom od of mass M is suppoted by two vetical stings, as shown below. Find the tension in the emaining sting immediately afte one of the stings
More informationIntroduction to Nuclear Forces
Intoduction to Nuclea Foces One of the main poblems of nuclea physics is to find out the natue of nuclea foces. Nuclea foces diffe fom all othe known types of foces. They cannot be of electical oigin since
More information3.012 Fund of Mat Sci: Bonding Lecture 5/6. Comic strip removed for copyright reasons.
3.12 Fund of Mat Sci: Bonding Lectue 5/6 THE HYDROGEN ATOM Comic stip emoved fo copyight easons. Last Time Metal sufaces and STM Diac notation Opeatos, commutatos, some postulates Homewok fo Mon Oct 3
More informationPHYSICS 4E FINAL EXAM SPRING QUARTER 2010 PROF. HIRSCH JUNE 11 Formulas and constants: hc =12,400 ev A ; k B. = hf " #, # $ work function.
PHYSICS 4E FINAL EXAM SPRING QUARTER 1 Fomulas and constants: hc =1,4 ev A ; k B =1/11,6 ev/k ; ke =14.4eVA ; m e c =.511"1 6 ev ; m p /m e =1836 Relativistic enegy - momentum elation E = m c 4 + p c ;
More informationIntroduction to Dielectric Properties and Magnetism
Intoduction to Dielectic opeties and Magnetism At the end of the last lectue we looked at some of the electical popeties of matte and intoduces the notions of electic field and electical conductivity.
More informationModeling Fermi Level Effects in Atomistic Simulations
Mat. Res. Soc. Symp. Poc. Vol. 717 Mateials Reseach Society Modeling Femi Level Effects in Atomistic Simulations Zudian Qin and Scott T. Dunham Depatment of Electical Engineeing, Univesity of Washington,
More informationMolecular dynamics simulation of ultrafast laser ablation of fused silica
IOP Publishing Jounal of Physics: Confeence Seies 59 (27) 1 14 doi:1.188/1742-6596/59/1/22 Eighth Intenational Confeence on Lase Ablation Molecula dynamics simulation of ultafast lase ablation of fused
More informationMobility of atoms and diffusion. Einstein relation.
Mobility of atoms and diffusion. Einstein elation. In M simulation we can descibe the mobility of atoms though the mean squae displacement that can be calculated as N 1 MS ( t ( i ( t i ( 0 N The MS contains
More informationMany Electron Atoms. Electrons can be put into approximate orbitals and the properties of the many electron systems can be catalogued
Many Electon Atoms The many body poblem cannot be solved analytically. We content ouselves with developing appoximate methods that can yield quite accuate esults (but usually equie a compute). The electons
More informationDiffusion and Transport. 10. Friction and the Langevin Equation. Langevin Equation. f d. f ext. f () t f () t. Then Newton s second law is ma f f f t.
Diffusion and Tanspot 10. Fiction and the Langevin Equation Now let s elate the phenomena of ownian motion and diffusion to the concept of fiction, i.e., the esistance to movement that the paticle in the
More information= e2. = 2e2. = 3e2. V = Ze2. where Z is the atomic numnber. Thus, we take as the Hamiltonian for a hydrogenic. H = p2 r. (19.4)
Chapte 9 Hydogen Atom I What is H int? That depends on the physical system and the accuacy with which it is descibed. A natual stating point is the fom H int = p + V, (9.) µ which descibes a two-paticle
More informationDEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS
DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS TSOKOS LESSON 10-1 DESCRIBING FIELDS Essential Idea: Electic chages and masses each influence the space aound them and that influence can be epesented
More informationNuclear models: Shell model
Lectue 3 Nuclea models: Shell model WS0/3: Intoduction to Nuclea and Paticle Physics,, Pat I Nuclea models Nuclea models Models with stong inteaction between the nucleons Liquid dop model α-paticle model
More information3.320: Lecture 6 (Feb ) Photos of Hartree, Fock, Hohenberg, Kohn, and Sham removed for copyright reasons.
3.30: Lectue 6 Feb 7 005 HARTREE-FOCK AND DFT Photos of Hatee, Fock, Hohenbeg, Kohn, and Sham emoved fo copyight easons. Feb 7 005 3.30 Atomistic Modeling of Mateials -- Geband Cede and Nicola Mazai Matix
More informationPHYS 172: Modern Mechanics. Fall Lecture 6 Fundamental Forces, Reciprocity Read
PHYS 172: Moden Mechanics Fall 2009 Lectue 6 Fundamental Foces, Recipocity Read 3.9 3.14 Exam 1 - Tuesday Septembe 15, 8:00-10:00 PM Elliott Hall of Music 1. The exam will be witten as a standad 1 hou
More informationAnyone who can contemplate quantum mechanics without getting dizzy hasn t understood it. --Niels Bohr. Lecture 17, p 1
Anyone who can contemplate quantum mechanics without getting dizzy hasn t undestood it. --Niels Boh Lectue 17, p 1 Special (Optional) Lectue Quantum Infomation One of the most moden applications of QM
More informationPhysical Chemistry II (Chapter 4 1) Rigid Rotor Models and Angular Momentum Eigenstates
Physical Chemisty II (Chapte 4 ) Rigid Roto Models and Angula Momentum Eigenstates Tae Kyu Kim Depatment of Chemisty Rm. 30 (tkkim@pusan.ac.k) http://cafe.nave.com/moneo76 SUMMAR CHAPTER 3 A simple QM
More information3.23 Electrical, Optical, and Magnetic Properties of Materials
MIT OpenCouseWae http://ocw.mit.edu 3.23 Electical, Optical, and Magnetic Popeties of Mateials Fall 27 Fo infomation about citing these mateials o ou Tems of Use, visit: http://ocw.mit.edu/tems. 3.23 Fall
More informationParticle Physics. From Monday: Summary. Lecture 9: Quantum Chromodynamics (QCD) q 2 m 2 Z. !q q!q q scattering
Paticle Physics Lectue 9: Quantum Chomodynamics (QCD)!Colou chage and symmety!gluons!qcd Feynman Rules!! scatteing!jets! 1 Fom Monday: Summay Weak Neutal Cuent Caied by the massive Z-boson: acts on all
More information5.111 Lecture Summary #6 Monday, September 15, 2014
5.111 Lectue Summay #6 Monday, Septembe 15, 014 Readings fo today: Section 1.9 Atomic Obitals. Section 1.10 Electon Spin, Section 1.11 The Electonic Stuctue of Hydogen. (Same sections in 4 th ed.) Read
More informationPlasmonics and non-local interactions from TDDFT: graphene and metal surfaces
Plasmonics and non-local inteactions fom TDDFT: gaphene and metal sufaces Thomas Olsen Cente fo Atomic-scale Mateials Design CAMD Depatment of Physics Technical Univesity of Denmak Outline Linea esponse
More information3.23 Electrical, Optical, and Magnetic Properties of Materials
MIT OpenCouseWae http://ocw.mit.edu 3.3 Electical, Optical, and Magnetic Popeties of Mateials Fall 7 Fo infomation about citing these mateials o ou Tems of Use, visit: http://ocw.mit.edu/tems. 3.3 Fall
More informationIntroduction to classical molecular dynamics (cont d) Mechanics of Ductile Materials
Fom nano to maco: Intoduction to atomistic modeling techniques IAP 2007 Intoduction to classical molecula dynamics (cont d) xxx Mechanics of Ductile Mateials Lectue 3 Makus J. Buehle Outline 1. Intoduction
More informationAnnihilation of Relativistic Positrons in Single Crystal with production of One Photon
Annihilation of Relativistic Positons in Single Cystal with poduction of One Photon Kalashnikov N.P.,Mazu E.A.,Olczak A.S. National Reseach Nuclea Univesity MEPhI (Moscow Engineeing Physics Institute),
More informationThree-dimensional systems with spherical symmetry
Thee-dimensiona systems with spheica symmety Thee-dimensiona systems with spheica symmety 006 Quantum Mechanics Pof. Y. F. Chen Thee-dimensiona systems with spheica symmety We conside a patice moving in
More informationChapter 9. Spintransport in Semiconductors. Spinelektronik: Grundlagen und Anwendung spinabhängiger Transportphänomene 1
Chapte 9 Spintanspot in Semiconductos : Gundlagen und Anwendung spinabhängige Tanspotphänomene 1 Winte 05/06 Why ae semiconductos of inteest in spintonics? They povide a contol of the chage as in conventional
More informationTeachers notes. Beyond the Thrills excursions. Worksheets in this book. Completing the worksheets
Beyond the Thills excusions Teaches notes Physics is the science of how the wold (and Univese) woks. Luna Pak Sydney is a lage hands-on physics laboatoy full of fee falling objects, otating systems and
More informationDEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS
DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS LSN 10-: MOTION IN A GRAVITATIONAL FIELD Questions Fom Reading Activity? Gavity Waves? Essential Idea: Simila appoaches can be taken in analyzing electical
More informationQuantum Mechanics II
Quantum Mechanics II Pof. Bois Altshule Apil 25, 2 Lectue 25 We have been dicussing the analytic popeties of the S-matix element. Remembe the adial wave function was u kl () = R kl () e ik iπl/2 S l (k)e
More informationSupporting information
Electonic Supplementay Mateial (ESI) fo Physical Chemisty Chemical Physics. This jounal is the Owne Societies 18 Suppoting infomation Nonstoichiometic oxides as a continuous homologous seies: linea fee-enegy
More informationSTUDY INTO THE INFLUENCE OF TEMPERATURE AND TIME FACTORS (160 C, 1-7 DAYS) ON HMX STRUCTURE (#254)
STUDY INTO THE INFLUENCE OF TEMPERATURE AND TIME FACTORS (160 C, 1-7 DAYS) ON HMX STRUCTURE (#254) T.Ye. Kisanova, V.N. Geman, A.M. Zlobin, T.G. Kiianova, Ye.S. Kozlova, V.N. Kolesnikova, S.P. Lobanova,
More informationField emission of Electrons from Negatively Charged Cylindrical Particles with Nonlinear Screening in a Dusty Plasma
Reseach & Reviews: Jounal of Pue and Applied Physics Field emission of Electons fom Negatively Chaged Cylindical Paticles with Nonlinea Sceening in a Dusty Plasma Gyan Pakash* Amity School of Engineeing
More informationCoupled Electromagnetic and Heat Transfer Simulations for RF Applicator Design for Efficient Heating of Materials
Coupled Electomagnetic and Heat Tansfe Simulations fo RF Applicato Design fo Efficient Heating of Mateials Jeni Anto 1 and Raj C Thiagaajan 2 * 1 Reseache, Anna Univesity, Chennai, 2 ATOA Scientific Technologies
More informationNuclear and Particle Physics - Lecture 20 The shell model
1 Intoduction Nuclea and Paticle Physics - Lectue 0 The shell model It is appaent that the semi-empiical mass fomula does a good job of descibing tends but not the non-smooth behaviou of the binding enegy.
More informationFE FORMULATIONS FOR PLASTICITY
G These slides ae designed based on the book: Finite Elements in Plasticity Theoy and Pactice, D.R.J. Owen and E. Hinton, 970, Pineidge Pess Ltd., Swansea, UK. Couse Content: A INTRODUCTION AND OVERVIEW
More informationChem 453/544 Fall /08/03. Exam #1 Solutions
Chem 453/544 Fall 3 /8/3 Exam # Solutions. ( points) Use the genealized compessibility diagam povided on the last page to estimate ove what ange of pessues A at oom tempeatue confoms to the ideal gas law
More informationc n ψ n (r)e ient/ h (2) where E n = 1 mc 2 α 2 Z 2 ψ(r) = c n ψ n (r) = c n = ψn(r)ψ(r)d 3 x e 2r/a0 1 πa e 3r/a0 r 2 dr c 1 2 = 2 9 /3 6 = 0.
Poblem {a} Fo t : Ψ(, t ψ(e iet/ h ( whee E mc α (α /7 ψ( e /a πa Hee we have used the gound state wavefunction fo Z. Fo t, Ψ(, t can be witten as a supeposition of Z hydogenic wavefunctions ψ n (: Ψ(,
More informationV7: Diffusional association of proteins and Brownian dynamics simulations
V7: Diffusional association of poteins and Bownian dynamics simulations Bownian motion The paticle movement was discoveed by Robet Bown in 1827 and was intepeted coectly fist by W. Ramsay in 1876. Exact
More informationSpring 2009 EE 710: Nanoscience and Engineering
Sping 009 EE 70: Nanoscience and Engineeing Pat 5: Chemical Inteactions at the Nanoscale Images and figues supplied fom Honyak, Dutta, Tibbals, and Rao, Intoduction to Nanoscience, CRC Pess, Boca Raton,
More informationPHYSICS 272H Electric & Magnetic Interactions
PHYSICS 7H Electic & Magnetic Inteactions Physics couse home page: http://www.physics.pudue.edu/academic-pogams/couses/all_couses.php Blackboad Lean: https://mycouses.pudue.edu/webapps/login/ Couse Content
More informationThe Time-Dependent Schrödinger Equation with applications to The Interaction of Light and Matter and The Selection Rules in Spectroscopy.
The Time-Dependent Schödinge Equation with applications to The Inteaction of Light and Matte and The Selection Rules in Spectoscopy. Lectue Notes fo Chemisty 45/746 by Macel Nooijen Depatment of Chemisty
More informationEntropy and Free Energy: Predicting the direction of spontaneous change The approach to Chemical equilibrium
Lectue 8-9 Entopy and Fee Enegy: Pedicting the diection of spontaneous change The appoach to Chemical equilibium Absolute entopy and the thid law of themodynamics To define the entopy of a compound in
More informationEE-145L Properties of Materials Laboratory
Univesity of Califonia at Santa Cuz Jack Baskin School of Engineeing EE-145L Popeties of Mateials Laboatoy Sping 2003 Holge Schmidt Developed by Ali Shakouti, based on the notes by Pof. Emily Allen, San
More informationStellar Structure and Evolution
Stella Stuctue and Evolution Theoetical Stella odels Conside each spheically symmetic shell of adius and thickness d. Basic equations of stella stuctue ae: 1 Hydostatic equilibium π dp dp d G π = G =.
More information1.1 THE ELECTRIC CHARGE
1.1 THE ELECTRIC CHARGE - In a dy day, one obseves "light spaks" when a wool pull is taken out o when the finges touch a metallic object. Aound the yea 1600, one classified these effects as electic phenomena.
More informationFUNDAMENTALS OF PHYSICS Vol. II - Qouantum-Mechanical Description Of Solids- Timothy B. Boykin QUANTUM-MECHANICAL DESCRIPTION OF SOLIDS
QUANTUM-MECHANICAL DESCRIPTION OF SOLIDS Timothy B. Boykin Depatment of Electical and Compute Engineeing, The Univesity of Alabama in Huntsville, USA Keywods: Bandstuctue, tight-binding, pseudopotential,
More informationPhotonic Crystals and Their Various Applications
Photonic Cystals and Thei Vaious Applications M Naci Inci Faculty of Engineeing & Natual Sciences Sabanci Univesity, Istanbul, Tukey What is a Photonic Cystal? A peiodic stuctue of dielectic medium on
More informationPhysics 862: Atoms, Nuclei, and Elementary Particles
Physics 86: Atoms, Nuclei, and Elementay Paticles Bian Bockelman Septembe 11, 008 Contents 1 Cental Field Poblems 1.1 Classical Teatment......................... 1. Quantum Teatment.........................
More informationVALLIAMMAI ENGINEERING COLLEGE
VALLIAMMAI ENGINEERING COLLEGE SRM Naga, Kattankulathu 603 203 DEPARTMENT OF PHYSICS QUESTION BANK II SEMESTER PH8253 - PHYSICS FOR ELECTRONICS ENGINEERING (Common to ECE, EEE, E&I) Regulation 2017 Academic
More informationRecent Advances in Chemical Engineering, Biochemistry and Computational Chemistry
Themal Conductivity of Oganic Liquids: a New Equation DI NICOLA GIOVANNI*, CIARROCCHI ELEONORA, PIERANTOZZI ARIANO, STRYJEK ROAN 1 DIIS, Univesità Politecnica delle ache, 60131 Ancona, ITALY *coesponding
More informationElectromagnetic scattering. Graduate Course Electrical Engineering (Communications) 1 st Semester, Sharif University of Technology
Electomagnetic scatteing Gaduate Couse Electical Engineeing (Communications) 1 st Semeste, 1390-1391 Shaif Univesity of Technology Geneal infomation Infomation about the instucto: Instucto: Behzad Rejaei
More informationWith What Does It Mean the Organic Chemical Phenomena Are Solved?
With What Does It Mean the Oganic Chemical Phenomena Ae Solved? Let me explain the meaning of this title quoting a simple example. Aniline has otho and paa oientation natue and nitobenzene has meta oientation
More informationSingle Particle State AB AB
LECTURE 3 Maxwell Boltzmann, Femi, and Bose Statistics Suppose we have a gas of N identical point paticles in a box of volume V. When we say gas, we mean that the paticles ae not inteacting with one anothe.
More informationThe second law of thermodynamics - II.
Januay 21, 2013 The second law of themodynamics - II. Asaf Pe e 1 1. The Schottky defect At absolute zeo tempeatue, the atoms of a solid ae odeed completely egulaly on a cystal lattice. As the tempeatue
More informationObjectives. We will also get to know about the wavefunction and its use in developing the concept of the structure of atoms.
Modue "Atomic physics and atomic stuctue" Lectue 7 Quantum Mechanica teatment of One-eecton atoms Page 1 Objectives In this ectue, we wi appy the Schodinge Equation to the simpe system Hydogen and compae
More informationm = mass of the particle E =
Kumpula 18.10.2010 The basic ideas of quantum physics Quantum mechanics makes nano diffeent Risto Nieminen COMP/Applied Physics Aalto Univesity School of Science and Technology 1. Matte has both wave-
More informationQuantum Mechanics and the Cool Science of Hydrogen. drogen roperties for nergy esearch
Quantum Mechanics and the Cool Science of Hydogen H H Y P E R dogen opeties fo negy eseach In this talk: 1. An intoduction. Why hydogen? 3. Quantum Mechanics 4. Equations of State 5. Mixtues Jacob Leachman,
More informationThe Poisson bracket and magnetic monopoles
FYST420 Advanced electodynamics Olli Aleksante Koskivaaa Final poject ollikoskivaaa@gmail.com The Poisson backet and magnetic monopoles Abstact: In this wok magnetic monopoles ae studied using the Poisson
More informationThe Clausius-Mossotti Equation
The Clausius-Mossotti quation Ottaviano Mossotti (1850) and Rudolf Clausius (1879) Jason Rich McKinley Goup Summe Reading Club Familia Results and Famous Papes August 17, 2007 Ottaviano Fabizio Mossotti
More informationChapter 13 Gravitation
Chapte 13 Gavitation In this chapte we will exploe the following topics: -Newton s law of gavitation, which descibes the attactive foce between two point masses and its application to extended objects
More informationProblem Set 10 Solutions
Chemisty 6 D. Jean M. Standad Poblem Set 0 Solutions. Give the explicit fom of the Hamiltonian opeato (in atomic units) fo the lithium atom. You expession should not include any summations (expand them
More informationDownloaded from
Chapte Notes Subject: Chemisty Class: XI Chapte: Themodynamics Top concepts 1. The banch of science which deals with study of diffeent foms of enegy and thei inteconvesion is called themodynamics. 2. A
More informationChapter 6: Rotational and Rovibrational Spectra. A) General discussion of two- body problem with central potential
Fall 4 Chapte 6: Rotational and Rovibational Specta... 75 Diffeent Appoximations... 8 Spectum fo Hamonic Oscillato + Rigid Rotato... 8 Polyatomic Molecules... 84 Hamonic Oscillato + Rigid Roto Model to
More informationRight-handed screw dislocation in an isotropic solid
Dislocation Mechanics Elastic Popeties of Isolated Dislocations Ou study of dislocations to this point has focused on thei geomety and thei ole in accommodating plastic defomation though thei motion. We
More informationCalculation of Quark-antiquark Potential Coefficient and Charge Radius of Light Mesons
Applied Physics Reseach ISSN: 96-9639 Vol., No., May E-ISSN: 96-9647 Calculation of Quak-antiquak Potential Coefficient and Chage Radius of Light Mesons M.R. Shojaei (Coesponding autho ) Depatment of Physics
More informationPhysics 235 Chapter 5. Chapter 5 Gravitation
Chapte 5 Gavitation In this Chapte we will eview the popeties of the gavitational foce. The gavitational foce has been discussed in geat detail in you intoductoy physics couses, and we will pimaily focus
More information2 Lecture 2: The Bohr atom (1913) and the Schrödinger equation (1925)
1 Lectue 1: The beginnings of quantum physics 1. The Sten-Gelach expeiment. Atomic clocks 3. Planck 1900, blackbody adiation, and E ω 4. Photoelectic effect 5. Electon diffaction though cystals, de Boglie
More informationFoundations of Chemical Kinetics. Lecture 9: Generalizing collision theory
Foundations of Chemical Kinetics Lectue 9: Genealizing collision theoy Mac R. Roussel Depatment of Chemisty and Biochemisty Spheical pola coodinates z θ φ y x Angles and solid angles θ a A Ω θ=a/ unit:
More informationKey Questions. ECE 340 Lecture 4 : Bonding Forces and Energy Bands 1/28/14. Class Outline: v Crystal Diffraction Crystal Bonding
ECE 340 Lectue 4 : onding Foces and Enegy ands v Cystal Diffaction Class Outline: Things you should know when you leave Key Questions Why is the oh model useful? What is the Schödinge equation? What is
More informationarxiv: v1 [physics.gen-ph] 18 Aug 2018
Path integal and Sommefeld quantization axiv:1809.04416v1 [physics.gen-ph] 18 Aug 018 Mikoto Matsuda 1, and Takehisa Fujita, 1 Japan Health and Medical technological college, Tokyo, Japan College of Science
More informationPHYSICS 272 Electric & Magnetic Interactions. Prof. Andrew Hirsch Room: 178, Phone: 42218
PHYSICS 7 Electic & Magnetic Inteactions Pof. Andew Hisch Hisch@pudue.edu Room: 78, Phone: 48 Couse Content This couse deals with electic and magnetic inteactions, which ae cental to the stuctue of matte,
More informationEXAM NMR (8N090) November , am
EXA NR (8N9) Novembe 5 9, 9. 1. am Remaks: 1. The exam consists of 8 questions, each with 3 pats.. Each question yields the same amount of points. 3. You ae allowed to use the fomula sheet which has been
More informationCharges, Coulomb s Law, and Electric Fields
Q&E -1 Chages, Coulomb s Law, and Electic ields Some expeimental facts: Expeimental fact 1: Electic chage comes in two types, which we call (+) and (). An atom consists of a heavy (+) chaged nucleus suounded
More informationMethods to describe direct reactions. II. Transfer reactions. Distorted wave approximations and beyond. N.K. Timofeyuk University of Surrey, UK
Methods to descie diect eactions. II. Tansfe eactions. Distoted wave appoximations and eyond. N.K. Timofeyuk Univesity of Suey UK Content Exact amplitude and distoted waves on appoximation Ovelap functions
More information7.2. Coulomb s Law. The Electric Force
Coulomb s aw Recall that chaged objects attact some objects and epel othes at a distance, without making any contact with those objects Electic foce,, o the foce acting between two chaged objects, is somewhat
More informationQuantum Chemistry Notes:
Quantum Chemisty otes: Hatee-Fock equations The Hatee-Fock method is the undelying appoximation to nealy all methods of computational chemisty, both ab initio and semi-empiical. Theefoe, a clea undestanding
More informationParticle Systems. University of Texas at Austin CS384G - Computer Graphics Fall 2010 Don Fussell
Paticle Systems Univesity of Texas at Austin CS384G - Compute Gaphics Fall 2010 Don Fussell Reading Requied: Witkin, Paticle System Dynamics, SIGGRAPH 97 couse notes on Physically Based Modeling. Witkin
More informationPartition Functions. Chris Clark July 18, 2006
Patition Functions Chis Clak July 18, 2006 1 Intoduction Patition functions ae useful because it is easy to deive expectation values of paametes of the system fom them. Below is a list of the mao examples.
More informationThermophysical properties of dunite rocks as a function of temperature along with the prediction of effective thermal conductivity
Vol.2, No.6, 626-630 (200) http://dx.doi.og/0.4236/ns.200.26077 Natual Science Themophysical popeties of dunite ocks as a function of tempeatue along with the pediction of effective themal conductivity
More informationIntroduction to Mathematical Statistics Robert V. Hogg Joeseph McKean Allen T. Craig Seventh Edition
Intoduction to Mathematical Statistics Robet V. Hogg Joeseph McKean Allen T. Caig Seventh Edition Peason Education Limited Edinbugh Gate Halow Essex CM2 2JE England and Associated Companies thoughout the
More informationDetermining solar characteristics using planetary data
Detemining sola chaacteistics using planetay data Intoduction The Sun is a G-type main sequence sta at the cente of the Sola System aound which the planets, including ou Eath, obit. In this investigation
More informationEnergy Levels Of Hydrogen Atom Using Ladder Operators. Ava Khamseh Supervisor: Dr. Brian Pendleton The University of Edinburgh August 2011
Enegy Levels Of Hydogen Atom Using Ladde Opeatos Ava Khamseh Supeviso: D. Bian Pendleton The Univesity of Edinbugh August 11 1 Abstact The aim of this pape is to fist use the Schödinge wavefunction methods
More informationRigid Body Dynamics 2. CSE169: Computer Animation Instructor: Steve Rotenberg UCSD, Winter 2018
Rigid Body Dynamics 2 CSE169: Compute Animation nstucto: Steve Rotenbeg UCSD, Winte 2018 Coss Poduct & Hat Opeato Deivative of a Rotating Vecto Let s say that vecto is otating aound the oigin, maintaining
More informationQuantum theory of angular momentum
Quantum theoy of angula momentum Igo Mazets igo.mazets+e141@tuwien.ac.at (Atominstitut TU Wien, Stadionallee 2, 1020 Wien Time: Fiday, 13:00 14:30 Place: Feihaus, Sem.R. DA gün 06B (exception date 18 Nov.:
More informationConfined Self-Assembly of Block Copolymers
Confined Self-Assembly of Block Copolymes An-Chang Shi Depatment of Physics & Astonomy McMaste Univesity Hamilton, Ontaio Canada Collaboatos: Bin Yu and Baohui Li, Nankai Univesity Peng Chen and Haojun
More informationIdentification of the degradation of railway ballast under a concrete sleeper
Identification of the degadation of ailway ballast unde a concete sleepe Qin Hu 1) and Heung Fai Lam ) 1), ) Depatment of Civil and Achitectual Engineeing, City Univesity of Hong Kong, Hong Kong SAR, China.
More informationInteratomic Forces. Overview
Inteatomic Foces Oveview an de Walls (shot ange ~1/ 6, weak ~0.010.1 e) Ionic (long ange, ~1/, stong ~510 e) Metallic (no simple dependence, ~0.1e) Covalent (no simple dependence, diectional,~3 e) Hydogen
More informationThe tunneling spectrum of Einsein Born-Infeld Black Hole. W. Ren2
Intenational Confeence on Engineeing Management Engineeing Education and Infomation Technology (EMEEIT 015) The tunneling spectum of Einsein Bon-Infeld Black Hole J Tang1 W Ren Y Han3 1 Aba teaches college
More information12.1 INTRODUCTION: STATES OF MANY-PARTICLE SYSTEMS
Chapte 1 2 : Many- Paticle Systems Chapte 12: Many-Paticle Systems...186 12.1 Intoduction: States of Many-Paticle Systems...186 12.2 Systems Divisible into Independent Subsystems...188 12.2.1 Distinguishable
More informationPHYSICS 1210 Exam 2 University of Wyoming 14 March ( Day!) points
PHYSICS 1210 Exam 2 Univesity of Wyoming 14 Mach ( Day!) 2013 150 points This test is open-note and closed-book. Calculatos ae pemitted but computes ae not. No collaboation, consultation, o communication
More informationNuclear size corrections to the energy levels of single-electron atoms
Nuclea size coections to the enegy levels of single-electon atoms Babak Nadii Nii a eseach Institute fo Astonomy and Astophysics of Maagha (IAAM IAN P. O. Box: 554-44. Abstact A study is made of nuclea
More informationQUASI-STATIONARY ELECTRON STATES IN SPHERICAL ANTI-DOT WITH DONOR IMPURITY * 1. INTRODUCTION
ATOMIC PHYSICS QUASI-STATIONARY ELECTRON STATES IN SPHERICAL ANTI-DOT ITH DONOR IMPURITY * V. HOLOVATSKY, O. MAKHANETS, I. FRANKIV Chenivtsi National Univesity, Chenivtsi, 581, Ukaine, E-mail: ktf@chnu.edu.ua
More information3.012 Fund of Mat Sci: Bonding Lecture 11. The future of electronics? A pentacene molecule deposited on SiO 2. Image removed for copyright reasons.
3.012 Fund of Mat Sci: Bonding Lectue 11 BONDING IN MOLECULES The futue of electonics? A pentacene molecule deposited on SiO 2 as a thin film Image emoved fo copyight easons. 3.012 Fundamentals of Mateials
More informationPHYSICS 272 Electric & Magnetic Interactions. Prof. Andrew Hirsch Room: 178, Phone: 42218
PHYSICS 7 Electic & Magnetic Inteactions Pof. Andew Hisch Hisch@pudue.edu Room: 78, Phone: 48 Couse Content This couse deals with electic and magnetic inteactions, which ae cental to the stuctue of matte,
More information