m = mass of the particle E =
|
|
- Tobias Beasley
- 5 years ago
- Views:
Transcription
1 Kumpula 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- and paticle-like popeties. - Wavelength λ = h 2mE h = Planck s constant 34 Js m = mass of the paticle E = its kinetic enegy
2 In themal equilibium, 23 1 k B = JK E = 3 2 Quantum mechanics is impotant when a = k B T Boltzmann s constant 19 J = ev 300 K = 25,8 mev λ intepaticle spacing o device size. Fo electons, nealy always. Fo potons, sometimes (especially at low tempeatues). Fo He atoms, at vey low tempeatues Fo othe atoms, at even lowe tempeatues (e.g. cold atomic gases, BEC) Inside nuclei and nucleons: diffeent length and enegy scales! a Electon Wave Intefeence Expeimental EVIDENCE Whethe it is light, o electons, the Double Slit Diffaction expeiment shows that in BOTH cases intefeence effects occu! What about in the opposite case? Is light made up of paticles? The expeimental evidence says YES! This is Einstein s photoelectic effect. 1 ( mv 2 2 ) max = hf φ
3 Wave-like popeties: Diffaction Scatteing Uncetainty pinciple Coheence Quantum confinement, zeo-point enegy Paticle-like popeties: Single-paticle counting Scatteing Ballistic tanspot The Bizae Wold of Quantum UNCERTAINTY The quantum wold is pobabilistic. This is decibed by Heisenbeg s Uncetainty Pinciple. The uncetainty elations ae: Δ x Δ p h 2 Δ E Δ t h 2 Notice that the uncetainty pinciple is unimpotant to macoscopic objects since Planck's constant, h, is so small (of ode ). Fo example, the uncetainty in position of a thown baseball is millimetes!
4 QUANTUM WORLD weid = counteintuitive : wave-paticle dualism inheently paallel quantum computing phase infomation many-paticle symmety/antisymmety mathematical desciption of electons vey complex ( femion sign poblem ) coupling to (classical) envionments decoheence dissipation
5 E min = Quantum confinement h π ml Enegy E min L
6
7 2. Moe quantum popeties Paticles (e.g. electons) have intenal degees of feedom : Spin Magnetism Many physical popeties ae quantized, i.e. only discete values ae possible, e.g. - Enegy levels specta (tansitions between enegy levels) - Angula momentum - Conductivity -Magneticflux - Voticity (in quantum liquids) - etc. The popeties of of the quantum paticles ae descibed by the Schödinge equation ( wave equation ) the wave function ψ (, t) The wave function descibing seveal paticles is eithe symmetic o antisymmetic with espect to paticle exchange quantum statistics, femions (such as electons) and bosons (such as photons (light quanta) o some light atoms)
8 The wave function can be intepeted as the pobability of finding the system (o an obsevable) in a given state. Fo example, the electon density 2 ), ( ), ( t t n ψ = ), ( ), ( ), ( t t H dt t d i h ψ ψ = Time evolution: Hamilton opeato: ), ( t V m H h + = Schödinge wave equation + bounday conditions Stationay eigenstates ) n ( ψ Geneal state is a supeposition of the eigenstates ) ( ) ( ), ( t c t n n n ψ ψ = Quantum infomation and computing
9 Quantum physics can be completely maied with special elativity: quantum electodynamics (QED). Not with geneal elativity (gavity), but the enegy scale is lage by a facto of Standad model : QED + quantum chomodynamics (QCD). Challenge: many inteacting paticles - collective popeties (e.g. feomagnetism) - emegent phenomena (e.g. supeconductivity) - macoscopic quantum effects (e.g. supefluidity) Coulomb inteaction
10 Playing with Atomic Lego But I am not afaid to conside the final question as to whethe, ultimately in the geat futue we can aange the atoms the way we want; the vey atoms,, all the way down! All things ae made of atoms. Electons ae the glue. - Richad P. Feynman, Linus Pauling, 1962 RICHARD FEYNMAN CONDENSED MATTER PHYSICS AND CHEMISTRY
11 NANOSCIENCE: Thee Is Plenty of Room at the Bottom Cental paadigms fo Condensed Matte Physics Weakly inteacting electons Stongly inteacting electons Richad P. Feynman Decembe 1959 Femi-Landau theoy Quasipaticles Band theoy Spin fluctuations Mixed-valence behavio Andeson and Kondo esonances How do we wite small? Infomation on a small scale Bette electon micoscopes The mavellous biological system Miniatuizing the compute Miniatuization by evapoation Poblems of lubication A hunded tiny hands Reaanging the atoms Atoms in a small wold 10-9 m BCS supeconductivity Exotic supeconductivity Disode-induced localization Wigne cystallization Intege QHE Factional QHE Fantastic testbed fo many-body phenomena: cold atoms in optical lattices.
12 Cental paadigms fo CMP (contd.) Cental paadigms fo CMP (contd.) Inteacting atoms Reductionist appoach: Quantum mechanics and electomagnetic inteactions Elementay excitations Emegence: phonons, plasmons, magnons, spinons etc. Response functions Gound state Stuctue-popety elationships Phase stability and tansitions Dynamics and excitations Spectoscopy Reactions Fom chemical bonds to bands Collective phenomena Equilbium tanspot Non-equilibium and dissipation Density-functional theoies Multiscale models Entanglement and decoheence These two paadigms can be linked.
13 Designing with Conventional ATOMS Atomic clustes have supising popeties at the nanoscale! To undestand the chemical bond, we need the machiney of quantum physics. Electons ae the glue. They behave quantum-mechanically and give ise to the vaiety of chemical bonds: -The ionicbond - The covalent bond - The metallic bond - The hydogen bond - The van de Waals bond Single phosphous atoms implanted into a silicon substate.
14 Small is diffeent: Non-scalable size egion the nanoscale mateials and stuctues have new, functional popeties Popety N α no. of atoms/molecules N
15 NANOSCIENCE AND TECHNOLOGY: HANDSHAKING OF The thee pillas of nanoscience and -technology quantum and classical phenomena equilibium and non-equilibium phenomena top-down and bottom-up appoaches eductionist and emegent viewpoints ( moe is diffeent ) Manufactue and manipulation top-down : lithogaphy bottom-up : self-assembly Chaacteisation, imaging and pobing SPM TEM PES Theoy, modelling and simulation Pedictive computation of physical, chemical and biological functions Pocess design Intepetation of pobe data Computational nanoscience
16 mako - mm TOP-DOWN Novel Nanosystems miko - μm nano - nm poikkitieteellinen ja -teknologinen nanotutkimus takkuusmanipulointi mikoelektoniikka litogafia etsaus kasvatus BOTTOM-UP itseoganisoituvuus kemiallinen synteesi molekyylisuunnittelu SPM-manipulointi Magnetic multilayes : Giant Magnetoesistance
17 Exotic Quantum Systems WELCOME TO THEWORLD OF ARTIFICIAL ATOMS! QUANTUM DOTS! FULLY TUNABLE SOLID STATE DEVICES Electons confined in a vey small space by an electostatic potential. CONFINEMENT = ATOM-LIKE PROPERTIES B Quantum Rings and things... Have vey stange quantum popeties, such as pesistent cuents, when a magnetic field is applied. Also inteesting magnetism which may be applied in computing.
18 Atoms tapped in Optical Lattices Atoms tapped in optical potentials. The optical potentials can be changed and theefoe the atificial atomic stuctue can also be changed. This gives us geate design feedom to ceate new nanoscale devices, beyond that which we could get fom the peiodic table elements.
19
20 Atomic Foce Micoscopy: Tip Change Imaging F - t Tip Change Imaging Ca 2+
21 Biowold is also a nanowold. Electophoesis of nanocolloids Lipid membanes
22 Quantum dots in biology: changing colous Quantum physics in biology: olfaction The biggest thing we can smell is atoms lage. Shape does not solve it: lock and key not enough. Feocene vs. nickeloscene: exactly the same stuctue, smell vey diffeent! Explanation: inelastic electon tunnelling fom the molecules. Othe examples: poton tansfe concentation gadient of potons acoss cell membanes
23 Quantum wies: the quantization of conductivity Au quantum wie, STM Quantum of conductance: G 0 = 2e 2 /h = 1/12.9 kw, elongation foce oscillations C 60 (fulleene) on a metal suface The mophology of Pt suface M.R. Soensen et al., Phys. Rev. B. 57, 3283 (1998) G. Rubio, N. Agaït, and S. Vieia, Phys. Rev. Lett. 76, 2302 (1996) Gaphite suface Tiblock-copolyme
24 Mooe s Law Godon Mooe Founde of Intel Inc. Electonics Magazine, 1965 Nanoelectonics and spintonics as a new platfom fo infomation technology: a possibility to extend Mooe s Law into the futue. The numbe of switches on a silicon chips will double evey 12 months (late evised to 18 months)
25 The shinking featue size One needs new insulato mateials HfO 2 90 nm pocess capacitance 1 leakage cuent 1 capacitance 1.6 leakage cuent < 0.01
26 Cabon nanotube as a quantum wie Single-electon tansisto Etching of silicon sufaces (Miguel Gosalvez) Nanoscale Au clustes ae eactive!
27 Mono-laye Potected Gold Nanoclustes Rautaoksidi-nanopatikkeli Univ. Califonia Bekeley PbSe-kvanttipiste elektonimikoskopia
28 Metallinen, yksiseinäinen hiilinanoputki (SWNCT) ultamikoskopia : - alle 0.1 nanometin takkuus a) elektonidiffaktiokuva kieteisyys b) tansmissioelektonimikoskopia Aalto/Uusien Mateiaalien Keskus (Esko Kauppinen) α = d = 2.07 nm Kaksosaja <110>-suunnassa STiO 3 -peovskiitissa ( m, n ) = (21, 9) d (21,9) = 2.09 nm α (21,9) = 17.0
29 Nobel 2010: Gaphene One atomic laye of hexagonal cabon
30 Samsung Electonics
Quantum mechanics makes nano different
Kumpula 18.10.2010 Quantum mechanics makes nano different Risto Nieminen COMP/Applied Physics Aalto University School of Science and Technology The basic ideas of quantum physics 1. Matter has both wave-
More informationλ = m = mass of the particle E = The basic ideas of quantum physics Quantum mechanics makes nano different
Kumpula 18.10.010 The basic ideas of quantum physics Quantum mechanics makes nano different Risto Nieminen COMP/Applied Physics Aalto University School of Science and Technology 1. Matter has both wave-
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 informationFrom Atoms to Materials: Predictive Theory and Simulations. Materials are everywhere
Fom Atoms to Mateials: Pedictive Theoy and Simulations Intoduction Ale Stachan stachan@pudue.edu School of Mateials Engineeing & Bick Nanotechnology Cente Pudue Univesity West Lafayette, Indiana USA Mateials
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 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 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 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 informationGermán Sierra Instituto de Física Teórica CSIC-UAM, Madrid, Spain
Gemán Siea Instituto de Física Teóica CSIC-UAM, Madid, Spain Wo in pogess done in collaboation with J. Lins and S. Y. Zhao (Univ. Queensland, Austalia) and M. Ibañez (IFT, Madid) Taled pesented at the
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 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 informationRydberg-Rydberg Interactions
Rydbeg-Rydbeg Inteactions F. Robicheaux Aubun Univesity Rydbeg gas goes to plasma Dipole blockade Coheent pocesses in fozen Rydbeg gases (expts) Theoetical investigation of an excitation hopping though
More informationGalilean Transformation vs E&M y. Historical Perspective. Chapter 2 Lecture 2 PHYS Special Relativity. Sep. 1, y K K O.
PHYS-2402 Chapte 2 Lectue 2 Special Relativity 1. Basic Ideas Sep. 1, 2016 Galilean Tansfomation vs E&M y K O z z y K In 1873, Maxwell fomulated Equations of Electomagnetism. v Maxwell s equations descibe
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 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 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 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 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 informationFI 2201 Electromagnetism
FI 2201 Electomagnetism Alexande A. Iskanda, Ph.D. Physics of Magnetism and Photonics Reseach Goup Electodynamics ELETROMOTIVE FORE AND FARADAY S LAW 1 Ohm s Law To make a cuent flow, we have to push the
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 information( n x ( ) Last Time Exam 3 results. Question. 3-D particle in box: summary. Modified Bohr model. 3-D Hydrogen atom. r n. = n 2 a o
Last Time Exam 3 esults Quantum tunneling 3-dimensional wave functions Deceasing paticle size Quantum dots paticle in box) This week s honos lectue: Pof. ad histian, Positon Emission Tomogaphy Tue. Dec.
More informationEM Boundary Value Problems
EM Bounday Value Poblems 10/ 9 11/ By Ilekta chistidi & Lee, Seung-Hyun A. Geneal Desciption : Maxwell Equations & Loentz Foce We want to find the equations of motion of chaged paticles. The way to do
More informationLecture 3.7 ELECTRICITY. Electric charge Coulomb s law Electric field
Lectue 3.7 ELECTRICITY Electic chage Coulomb s law Electic field ELECTRICITY Inteaction between electically chages objects Many impotant uses Light Heat Rail tavel Computes Cental nevous system Human body
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 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 informationDILUTE QUANTUM DROPLETS
DILUTE QUANTUM DROPLETS Auel Bulgac Phys. Rev. Lett. 89, 54 Quantum Fluids at T Liquid 4 He and He Electons but only embedded in an ion backgound BEC in alkali atoms and hydogen and the Femi-Diac countepats
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 informationNumerical solution of diffusion mass transfer model in adsorption systems. Prof. Nina Paula Gonçalves Salau, D.Sc.
Numeical solution of diffusion mass tansfe model in adsoption systems Pof., D.Sc. Agenda Mass Tansfe Mechanisms Diffusion Mass Tansfe Models Solving Diffusion Mass Tansfe Models Paamete Estimation 2 Mass
More informationPhysics 11 Chapter 20: Electric Fields and Forces
Physics Chapte 0: Electic Fields and Foces Yesteday is not ous to ecove, but tomoow is ous to win o lose. Lyndon B. Johnson When I am anxious it is because I am living in the futue. When I am depessed
More information( ) [ ] [ ] [ ] δf φ = F φ+δφ F. xdx.
9. LAGRANGIAN OF THE ELECTROMAGNETIC FIELD In the pevious section the Lagangian and Hamiltonian of an ensemble of point paticles was developed. This appoach is based on a qt. This discete fomulation can
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 informationAppendix B The Relativistic Transformation of Forces
Appendix B The Relativistic Tansfomation of oces B. The ou-foce We intoduced the idea of foces in Chapte 3 whee we saw that the change in the fou-momentum pe unit time is given by the expession d d w x
More informationElectrostatics. 3) positive object: lack of electrons negative object: excess of electrons
Electostatics IB 12 1) electic chage: 2 types of electic chage: positive and negative 2) chaging by fiction: tansfe of electons fom one object to anothe 3) positive object: lack of electons negative object:
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 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 informationDoublet structure of Alkali spectra:
Doublet stuctue of : Caeful examination of the specta of alkali metals shows that each membe of some of the seies ae closed doublets. Fo example, sodium yellow line, coesponding to 3p 3s tansition, is
More informationLocal Density Functional Theory for Superfluid Fermionic Systems. The Unitary Fermi Gas
Local Density unctional Theoy fo Supefluid emionic Systems The Unitay emi Gas Unitay emi gas in a hamonic tap Chang and Betsch, physics/070390 Outline: What is a unitay emi gas Vey bief/sewed summay of
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 informationA thermodynamic degree of freedom solution to the galaxy cluster problem of MOND. Abstract
A themodynamic degee of feedom solution to the galaxy cluste poblem of MOND E.P.J. de Haas (Paul) Nijmegen, The Nethelands (Dated: Octobe 23, 2015) Abstact In this pape I discus the degee of feedom paamete
More informationVoltage ( = Electric Potential )
V-1 of 10 Voltage ( = lectic Potential ) An electic chage altes the space aound it. Thoughout the space aound evey chage is a vecto thing called the electic field. Also filling the space aound evey chage
More informationLecture 4 Povh Krane Enge Williams
Lectue 4 Povh Kane Enge Williams the Deuteon 6. Ch. 4 Ch. Ch 3 d-wave admixtue 4..6 3.5 tenso foce 4..6 3.5 missing S state 4.4.5 3.4 isospin.3 6.7 3.4 Poblems on Lectue 4 What is the minimum photon enegy
More informationProjection Gravitation, a Projection Force from 5-dimensional Space-time into 4-dimensional Space-time
Intenational Jounal of Physics, 17, Vol. 5, No. 5, 181-196 Available online at http://pubs.sciepub.com/ijp/5/5/6 Science and ducation Publishing DOI:1.1691/ijp-5-5-6 Pojection Gavitation, a Pojection Foce
More information( ) ( ) Last Time. 3-D particle in box: summary. Modified Bohr model. 3-dimensional Hydrogen atom. Orbital magnetic dipole moment
Last Time 3-dimensional quantum states and wave functions Couse evaluations Tuesday, Dec. 9 in class Deceasing paticle size Quantum dots paticle in box) Optional exta class: eview of mateial since Exam
More information1.1 Problems with Waves Classically, EM radiation was well understood as a wave phenomenon, via Maxwell s theory. Problems arose around
0. Intoduction Recommended textbooks: Phillips, A. C. Intoduction to Quantum Mechanics Whiley Fench, A. P., Taylo, E. F, An Intoduction to Quantum Physics Thomas Nelson Othe books: Rae, A.I.M. Quantum
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 informationVortex Lattice in a Rotating Bose-Einstein Condensate
Votex Lattice in a Rotating Bose-Einstein Condensate By: Enikı Madaassy A Bose-Einstein condensate (BEC) is a state of matte of a system of bosons confined in an extenal potential. The atoms ae cooled
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 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 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 informationResearch by Jack Sarfatti, San Francisco, 7/28/09, 2:02 PM, page 1 of 6
Reseach by Jack Safatti, San Fancisco, 7/8/09, :0 PM, page 1 of 6 Wheele-Feynman Genealized Bohm Quantum Potential fo Open Fa-Fom-Equilibium Biological Dissipative Stuctues with Non-Unitay Post-Quantum
More informationCHEM1101 Worksheet 3: The Energy Levels Of Electrons
CHEM1101 Woksheet 3: The Enegy Levels Of Electons Model 1: Two chaged Paticles Sepaated by a Distance Accoding to Coulomb, the potential enegy of two stationay paticles with chages q 1 and q 2 sepaated
More informationcalculation the Hartree -Fock energy of 1s shell for some ions
JOURNAL OF KUFA PHYSICS Vol.6/ No. (4) calculation the Hatee -Fock enegy of s shell fo some ions Depatment of Physics, College of Science, Kufa Univesity E-mail : shaimanuclea@yahoo.com Abstact: In this
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 informationScattering in Three Dimensions
Scatteing in Thee Dimensions Scatteing expeiments ae an impotant souce of infomation about quantum systems, anging in enegy fom vey low enegy chemical eactions to the highest possible enegies at the LHC.
More informationElectric Field. y s +q. Point charge: Uniformly charged sphere: Dipole: for r>>s :! ! E = 1. q 1 r 2 ˆr. E sphere. at <0,r,0> at <0,0,r>
Electic Field Point chage: E " ˆ Unifomly chaged sphee: E sphee E sphee " Q ˆ fo >R (outside) fo >s : E " s 3,, at z y s + x Dipole moment: p s E E s "#,, 3 s "#,, 3 at
More informationMechanics Physics 151
Mechanics Physics 151 Lectue 5 Cental Foce Poblem (Chapte 3) What We Did Last Time Intoduced Hamilton s Pinciple Action integal is stationay fo the actual path Deived Lagange s Equations Used calculus
More informationPhysics 107 TUTORIAL ASSIGNMENT #8
Physics 07 TUTORIAL ASSIGNMENT #8 Cutnell & Johnson, 7 th edition Chapte 8: Poblems 5,, 3, 39, 76 Chapte 9: Poblems 9, 0, 4, 5, 6 Chapte 8 5 Inteactive Solution 8.5 povides a model fo solving this type
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 information1.2 Differential cross section
.2. DIFFERENTIAL CROSS SECTION Febuay 9, 205 Lectue VIII.2 Diffeential coss section We found that the solution to the Schodinge equation has the fom e ik x ψ 2π 3/2 fk, k + e ik x and that fk, k = 2 m
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 informationANALYSIS OF QUANTUM EIGENSTATES IN A 3-MODE SYSTEM
AAYSIS OF QUATUM EIGESTATES I A 3-MODE SYSTEM SRIHARI KESHAVAMURTHY AD GREGORY S. EZRA Depatment of Chemisty, Bake aboatoy Conell Univesity, Ithaca, Y 14853, USA. Abstact. We study the quantum eigenstates
More informationPhotoemission Spectroscopy Fundamental Aspects
Photoemission Spectoscopy Fundamental Aspects G. Stefani Dipatimento di Fisica E. Amaldi, Univesita Roma Te CISM Unita di Riceca di Roma 3 School G. Stefani 1 hν Basic Concepts - E, e K e εˆ E MAX e =
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 informationChapter Sixteen: Electric Charge and Electric Fields
Chapte Sixteen: Electic Chage and Electic Fields Key Tems Chage Conducto The fundamental electical popety to which the mutual attactions o epulsions between electons and potons ae attibuted. Any mateial
More informationQuantum Mechanics and Signed Particles, A New Formulation Has Come into Existence
Quantum Mechanics and Signed Paticles, A New Fomulation Has Come into Existence J. M. Sellie 1 *, I. Dimov 1 1 Institute of Infomation and Communication Technologies, Bulgaian Academy of Sciences, * coespondence
More informationSubstances that are liquids or solids under ordinary conditions may also exist as gases. These are often referred to as vapors.
Chapte 0. Gases Chaacteistics of Gases All substances have thee phases: solid, liquid, and gas. Substances that ae liquids o solids unde odinay conditions may also exist as gases. These ae often efeed
More informationc 2003, Michael Marder
Expeimental Detemination of Cystal Stuctues 1 8th Januay 003 c 003, Michael Made Histoy Expeiments and theoy in 191 finally evealed locations of atoms in cystalline solids. Essential ingedients: Theoy
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 informationPHYSICS 151 Notes for Online Lecture #36
Electomagnetism PHYSICS 151 Notes fo Online Lectue #36 Thee ae fou fundamental foces in natue: 1) gavity ) weak nuclea 3) electomagnetic 4) stong nuclea The latte two opeate within the nucleus of an atom
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 informationSUPPLEMENTARY INFORMATION
Sample pepaations Fe 0.5 Co 0.5 Si single cystal was gown by the floating zone technique. The phase puity and cation concentations wee checked by powde X-ay diffaction and Enegy Dispesive X-ay spectoscopy
More information( ) Bose-Einstein condensates in fast rotation. Rotating condensates. Landau levels for a rotating gas. An interesting variant: the r 2 +r 4 potential
Bose-instein condensates in fast otation Jean Dalibad Laboatoie Kastle Bossel cole nomale supéieue, Pais xp: Baptiste Battelie, Vincent Betin, Zoan Hadibabic, Sabine Stock Th: Amandine Aftalion, Xavie
More informationClass 2. Lesson 1 Stationary Point Charges and Their Forces. Basic Rules of Electrostatics. Basic Rules of Electrostatics
Lesson 1 Stationay Point Chages and Thei Foces Class Today we will: lean the basic chaacteistics o the electostatic oce eview the popeties o conductos and insulatos lean what is meant by electostatic induction
More informationUnit 7: Sources of magnetic field
Unit 7: Souces of magnetic field Oested s expeiment. iot and Savat s law. Magnetic field ceated by a cicula loop Ampèe s law (A.L.). Applications of A.L. Magnetic field ceated by a: Staight cuent-caying
More information221B Lecture Notes Scattering Theory I
Why Scatteing? B Lectue Notes Scatteing Theoy I Scatteing of paticles off taget has been one of the most impotant applications of quantum mechanics. It is pobably the most effective way to study the stuctue
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 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 informationPHYS 1441 Section 002. Lecture #3
PHYS 1441 Section 00 Chapte 1 Lectue #3 Wednesday, Sept. 6, 017 Coulomb s Law The Electic Field & Field Lines Electic Fields and Conductos Motion of a Chaged Paticle in an Electic Field Electic Dipoles
More information17.1 Electric Potential Energy. Equipotential Lines. PE = energy associated with an arrangement of objects that exert forces on each other
Electic Potential Enegy, PE Units: Joules Electic Potential, Units: olts 17.1 Electic Potential Enegy Electic foce is a consevative foce and so we can assign an electic potential enegy (PE) to the system
More informationA new force Magnetic force. Today. Force Fields: A disturbance of space. The correspondence of a loop of current and magnet.
Today A new foce Magnetic foce Announcements HW#6 and HW#7 ae both due Wednesday Mach 18th. Thanks to my being WAY behind schedule, you 2nd exam will be a take-home exam! Stay tuned fo details Even if
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 informationHigh-Impedance Surfaces with Graphene Patches as Absorbing. Electromagnetic Materials in Microwaves and Optics London, United Kingdom
Hih-Impedance Sufaces with Gaphene Patches as Absobin Stuctues at Micowaves A. B. Yakovlev, G. W. Hanson, and A. Mafi Thid Intenational Coness on Advanced Electomanetic Mateials in Micowaves and Optics
More informationNuclear reactions of heavy ions
Autho: Facultat de Física, Univesitat de Bacelona, Diagonal 645, 08028 Bacelona, Spain. Adviso: Xavie Vinyes Abstact: In this wok nuclea eactions of heavy ions ae studied, focusing on elastic scatteing.
More informationStructure of Hadrons. quarks d (down) s (strange) c (charm)
quaks Flavo A t t 0 S B T Q(e) Mc 2 (GeV) u (up) 1 3 1 2-1 2 0 0 0 0 2 3 0.002-0.008 d (down) 1 3 1 2 1 2 0 0 0 0-1 3 0.005-0.015 s (stange) 1 3 0 0-1 0 0 0-1 3 0.1-0.3 c (cham) 1 3 0 0 0 1 0 0 2 3 1.0-1.6
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 informationNovel Orbital Phases of Fermions in p-band Optical Lattices
Novel Obital Phases of Femions in p-band Optical Lattices Congjun Wu Depatment of Physics, UC San Diego W. C. Lee, C. Wu, S. Das Sama, in pepaation. C. Wu, PRL 0, 68807 008. C. Wu, PRL 00, 00406 008. C.
More informationPreliminary Exam: Quantum Physics 1/14/2011, 9:00-3:00
Peliminay Exam: Quantum Physics /4/ 9:-: Answe a total of SIX questions of which at least TWO ae fom section A and at least THREE ae fom section B Fo you answes you can use eithe the blue books o individual
More information763620SS STATISTICAL PHYSICS Solutions 2 Autumn 2012
763620SS STATISTICAL PHYSICS Solutions 2 Autumn 2012 1. Continuous Random Walk Conside a continuous one-dimensional andom walk. Let w(s i ds i be the pobability that the length of the i th displacement
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 informationConventional Paper-I (a) Explain the concept of gradient. Determine the gradient of the given field: ( )
EE-Conventional Pape-I IES-013 www.gatefoum.com Conventional Pape-I-013 1. (a) Eplain the concept of gadient. Detemine the gadient of the given field: V ρzsin φ+ z cos φ+ρ What is polaization? In a dielectic
More informationHawking Radiation. Alex Fontana
Hawking Radiation Alex Fontana In this epot the aim is to undestand the behaviou of a Schwazshild Black Hole in a context whee quantum field fluctuations ae taken into account. We ae going to see how to
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 informationSupplementary Figure 1. Circular parallel lamellae grain size as a function of annealing time at 250 C. Error bars represent the 2σ uncertainty in
Supplementay Figue 1. Cicula paallel lamellae gain size as a function of annealing time at 50 C. Eo bas epesent the σ uncetainty in the measued adii based on image pixilation and analysis uncetainty contibutions
More informationMAGNETIC FIELD AROUND TWO SEPARATED MAGNETIZING COILS
The 8 th Intenational Confeence of the Slovenian Society fo Non-Destuctive Testing»pplication of Contempoay Non-Destuctive Testing in Engineeing«Septembe 1-3, 5, Potoož, Slovenia, pp. 17-1 MGNETIC FIELD
More informationIntroduction to Arrays
Intoduction to Aays Page 1 Intoduction to Aays The antennas we have studied so fa have vey low diectivity / gain. While this is good fo boadcast applications (whee we want unifom coveage), thee ae cases
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 informationOn the Sun s Electric-Field
On the Sun s Electic-Field D. E. Scott, Ph.D. (EE) Intoduction Most investigatos who ae sympathetic to the Electic Sun Model have come to agee that the Sun is a body that acts much like a esisto with a
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 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 informationLecture 5 Solving Problems using Green s Theorem. 1. Show how Green s theorem can be used to solve general electrostatic problems 2.
Lectue 5 Solving Poblems using Geen s Theoem Today s topics. Show how Geen s theoem can be used to solve geneal electostatic poblems. Dielectics A well known application of Geen s theoem. Last time we
More information