EE243 Advanced Electromagnetic Theory Lec # 22 Scattering and Diffraction. Reading: Jackson Chapter 10.1, 10.3, lite on both 10.2 and 10.
|
|
- Damian Harris
- 5 years ago
- Views:
Transcription
1 Appid M Fa 6, Nuuth Lctu # V //6 43 Advancd ctomagntic Thoy Lc # Scatting and Diffaction Scatting Fom Sma Obcts Scatting by Sma Dictic and Mtaic Sphs Coction of Scatts Sphica Wav xpansions Scaa Vcto Rading: Jackson Chapt.,.3, it on both. and.4 Copyight 6 Rgnts of Univsity of Caifonia
2 Appid M Fa 6, Nuuth Lctu # V //6 Ovviw Scatting is simia to adiation but oftn quis simutanousy moding th cation of poaization and cunts fom stimuation by an xtna souc. Sma scatts a tatd by dipo momnts. Intmdiat scatts qui xpansion in many sphica hamonics. Lag scatts can b tatd by appoximation in vaious scaa and vctod diffaction intgas Copyight 6 Rgnts of Univsity of Caifonia
3 Appid M Fa 6, Nuuth Lctu # V //6 Scatting by Dipos Inducd in Sma Scatts n n Incidnt fid is in diction n and has poaization Thy induc ctic and magntic dipo momnts Scattd fid is in diction n and has poaization Not that fo th fa fid th a two choics fo ach of and but on choic ativ to th pan fomd by n and n Copyight 6 Rgnts of Univsity of Caifonia 3
4 Appid M Fa 6, Nuuth Lctu # V //6 Scatting by Dipos Inducd in Sma Scatts H p m H sc sc nˆ 4πε iknˆ ˆ n k sc Z x Z inducd _ ctic _ dipo inducd _ magntic _ dipo ik [( nˆ p) n n m / c] Jackson..A Incidnt fids induc ctic and magntic dipo momnts Fa fids fom a thn found fom ths momnts Copyight 6 Rgnts of Univsity of Caifonia 4
5 Appid M Fa 6, Nuuth Lctu # V //6 Diffntia Scatting Coss Sction dσ dω dσ dω ( nˆ, ˆ; nˆ, ˆ ) ( nˆ, ˆ; nˆ, ˆ ) Z ˆ Z k ( 4πε ) 4 ˆ ˆ sc p + ( nˆ ˆ ) m / c n is in obsvation diction with poaization, whi idnt fux is in diction n with poaization. Dfind as th outgoing pow adiatd p unit soid ang dividd by th idnt pow p unit aa. It is atd to th bistatic coss sction. Thn spciaiz to th cas of th ctic and magntic dipo momnts of sma scatts. Intgating ov both poaizations and a angs givs th ffctiv aa of th scatt Copyight 6 Rgnts of Univsity of Caifonia 5
6 Copyight 6 Rgnts of Univsity of Caifonia 6 Appid M Fa 6, Nuuth Lctu # V //6 Scatting fom a Sma Dictic Sph Dipo p is in th diction of th idnt fid and qua to th static poaization (sam wight facto and popotiona to voum). Radiation is popotiona th obsvation poaization diction dottd with th idnt poaization. This givs cosθ in on ang and constant in φ. Stngth is 6-th pow of siz (voum squad) and 4-th pow ativ to siz in wavngths. (This xpains th cation of th bu sky succss of hoizontay poaizd sun gasss). Stongst and qua in fowad and backwad dictions. ( ) ˆ ˆ ˆ, ˆ ˆ; ˆ, 4 + Ω Ω + Ω + a k d d d a k n n d d a p ε ε π σ σ ε ε σ ε ε πε Jackson..B p p
7 Appid M Fa 6, Nuuth Lctu # V //6 Scatting fom a Sma p..c. Sph p m dσ dω 4πε a πa 3 3 ( ) ( ) ( ) 4 6 nˆ, ˆ; nˆ, ˆ k a ˆ ˆ nˆ ˆ nˆ ˆ H Jackson..C p and m Both xist A at ight angs Intf cohnty poduc a + b cosθ typ pattns ow fowad (/3) and high backwad (x) scatting Copyight 6 Rgnts of Univsity of Caifonia 7
8 Appid M Fa 6, Nuuth Lctu # V //6 dσ dω q F F ( q ) ( q ) ( nˆ, ˆ; nˆ, ˆ ) knˆ knˆ Coction of Scatts iq x i iq ( 4πε ) ( x x ) i k 4 [ p + ( n ) m c] ˆ ˆ ˆ / Assum p and m coctd fo bing insid mdia Sum ov a scatts uding ativ phas masud with spct to idnt diction n and scattd diction n F(q) is N (numb of scatts) in fowad diction and dops quicky to zo xcpt fo cysta stuctus with Bagg ffct. Can b usd to masu ang of intmocua focs that poduc dnsity fuxuations (citica opascnc). Copyight 6 Rgnts of Univsity of Caifonia iq x Jackson..D 8
9 Appid M Fa 6, Nuuth Lctu # V //6 Scaa Sphica Wav Rpsntation Ψ Ψ h h ( x, ω) f ( ) Y ( θ, φ) [ ] Y ( θ, φ) () () ( ) ( ( x, ω) A h + A h ) (), m, m i + [ ] ( ) ( h ) m m k ik m Soution to scaa wav quation Sphica Hamonics Y m (θ,φ) Radia vaiation dpnds ony on indx m Match bounday conditions on sufac(s) at fixd m Jackson..D Copyight 6 Rgnts of Univsity of Caifonia 9
10 Appid M Fa 6, Nuuth Lctu # V //6 Scaa Sphica Wav Rpsntation: xamps ik x ik x ik x x 4π x x ik i i ik J ( ) () k h ( k ) Y ( θ, φ ) Y ( θ, φ) Y ( θ, φ ) Y ( θ, φ) 4π J m < m ( + ) J Y ( γ ) Scaa Gn s Function Pan wav in two foms Rpac Numica Gid outsid obct (Mi Mthod) Tansation/otation in coodinat systms Addition Thom fo Sphica Hamonics Sph-Sph intactions > Copyight 6 Rgnts of Univsity of Caifonia m m m ( ) h Jackson 9.6,.3 m Numica Sphica Hamonic xpansion Outsid
11 Appid M Fa 6, Nuuth Lctu # V //6 L X H g f Vcto Sphica Wav Rpsntation i m ( ) ( θ, φ), m Z a, m A B ( + ) ( θ, φ) (, m) f X a (, m) a k (, m) f X + a (, m) () () ( ) ( ) h () () ( ) ( ) h LY + A + B m m h h g Opato L givs compact notation xpssd in tms of ctic and magntic mutipos Souc and Bounday conditions on sufac at fixd Radia and H componnt on a Sph a adquat Copyight 6 Rgnts of Univsity of Caifonia i k M m M X g Jackson.3 m X m
12 Appid M Fa 6, Nuuth Lctu # V //6 Vcto Sphica Wav Rpsntation: xamp Jackson.4 Tota fid sum of idnt and scattd xpand scattd fid Outgoing wavs (ony) outsid Both typs but no idint fid insid Rotationay symmtic m + and - (ony) Bounday conditions tan and H tan continuous on bounday of sph Tactab fo Conducting Sph (Mi) Dictic Sph? Usfu fo chcking numica simuatos Copyight 6 Rgnts of Univsity of Caifonia
E F. and H v. or A r and F r are dual of each other.
A Duality Thom: Consid th following quations as an xampl = A = F μ ε H A E A = jωa j ωμε A + β A = μ J μ A x y, z = J, y, z 4π E F ( A = jω F j ( F j β H F ωμε F + β F = ε M jβ ε F x, y, z = M, y, z 4π
More informationEffect of Ground Conductivity on Radiation Pattern of a Dipole Antenna
Intnationa Jouna of Coput and ctica ngining, Vo., No. 3, August 9 793-863 ffct of Gound Conductivity on Radiation Pattn of a Dipo Antnna Md. Shahidu Isa, Md. Shohidu Isa, S. Mb, I, Md. Shah Aa Abst This
More informationEE243 Advanced Electromagnetic Theory Lec # 23 Scattering and Diffraction. Reading: Jackson Chapter , lite
Applid M Fall 6, Nuruthr Lctur #3 Vr /5/6 43 Advancd lctromagntic Thory Lc # 3 cattring and Diffraction calar Diffraction Thory Vctor Diffraction Thory Babint and Othr Principls Optical Thorm ading: Jackson
More informationSchool of Electrical Engineering. Lecture 2: Wire Antennas
School of lctical ngining Lctu : Wi Antnnas Wi antnna It is an antnna which mak us of mtallic wis to poduc a adiation. KT School of lctical ngining www..kth.s Dipol λ/ Th most common adiato: λ Dipol 3λ/
More information1. Radiation from an infinitesimal dipole (current element).
LECTURE 3: Radiation fom Infinitsimal (Elmntay) Soucs (Radiation fom an infinitsimal dipol. Duality in Maxwll s quations. Radiation fom an infinitsimal loop. Radiation zons.). Radiation fom an infinitsimal
More informationFI 3103 Quantum Physics
7//7 FI 33 Quantum Physics Axan A. Iskana Physics of Magntism an Photonics sach oup Institut Tknoogi Banung Schoing Equation in 3D Th Cnta Potntia Hyognic Atom 7//7 Schöing quation in 3D Fo a 3D pobm,
More informationHydrogen atom. Energy levels and wave functions Orbital momentum, electron spin and nuclear spin Fine and hyperfine interaction Hydrogen orbitals
Hydogn atom Engy lvls and wav functions Obital momntum, lcton spin and nucla spin Fin and hypfin intaction Hydogn obitals Hydogn atom A finmnt of th Rydbg constant: R ~ 109 737.3156841 cm -1 A hydogn mas
More informationSources. My Friends, the above placed Intro was given at ANTENTOP to Antennas Lectures.
ANTENTOP- 01-008, # 010 Radiation fom Infinitsimal (Elmntay) Soucs Fl Youslf a Studnt! Da finds, I would lik to giv to you an intsting and liabl antnna thoy. Hous saching in th wb gav m lots thotical infomation
More informationAcoustics and electroacoustics
coustics and lctoacoustics Chapt : Sound soucs and adiation ELEN78 - Chapt - 3 Quantitis units and smbols: f Hz : fqunc of an acoustical wav pu ton T s : piod = /f m : wavlngth= c/f Sound pssu a : pzt
More information8 - GRAVITATION Page 1
8 GAVITATION Pag 1 Intoduction Ptolmy, in scond cntuy, gav gocntic thoy of plantay motion in which th Eath is considd stationay at th cnt of th univs and all th stas and th plants including th Sun volving
More informationAakash. For Class XII Studying / Passed Students. Physics, Chemistry & Mathematics
Aakash A UNIQUE PPRTUNITY T HELP YU FULFIL YUR DREAMS Fo Class XII Studying / Passd Studnts Physics, Chmisty & Mathmatics Rgistd ffic: Aakash Tow, 8, Pusa Road, Nw Dlhi-0005. Ph.: (0) 4763456 Fax: (0)
More informationMolecules and electronic, vibrational and rotational structure
Molculs and ctonic, ational and otational stuctu Max on ob 954 obt Oppnhim Ghad Hzbg ob 97 Lctu ots Stuctu of Matt: toms and Molculs; W. Ubachs Hamiltonian fo a molcul h h H i m M i V i fs to ctons, to
More informationThe angle between L and the z-axis is found from
Poblm 6 This is not a ifficult poblm but it is a al pain to tansf it fom pap into Mathca I won't giv it to you on th quiz, but know how to o it fo th xam Poblm 6 S Figu 6 Th magnitu of L is L an th z-componnt
More information5- Scattering Stationary States
Lctu 19 Pyscs Dpatmnt Yamou Unvsty 1163 Ibd Jodan Pys. 441: Nucla Pyscs 1 Pobablty Cunts D. Ndal Esadat ttp://ctaps.yu.du.jo/pyscs/couss/pys641/lc5-3 5- Scattng Statonay Stats Rfnc: Paagaps B and C Quantum
More informationPropagation of Current Waves along Quasi-Periodical Thin-Wire Structures: Accounting of Radiation Losses
Intaction Nots Not 6 3 May 6 Popagation of Cunt Wavs aong Quasi-Piodica Thin-Wi Stuctus: Accounting of Radiation Losss Jügn Nitsch and Sgy Tkachnko Otto-von-Guick-Univsity Magdbug Institut fo Fundamnta
More informationSolid state physics. Lecture 3: chemical bonding. Prof. Dr. U. Pietsch
Solid stat physics Lctu 3: chmical bonding Pof. D. U. Pitsch Elcton chag dnsity distibution fom -ay diffaction data F kp ik dk h k l i Fi H p H; H hkl V a h k l Elctonic chag dnsity of silicon Valnc chag
More informationFourier transforms (Chapter 15) Fourier integrals are generalizations of Fourier series. The series representation
Pof. D. I. Nass Phys57 (T-3) Sptmb 8, 03 Foui_Tansf_phys57_T3 Foui tansfoms (Chapt 5) Foui intgals a gnalizations of Foui sis. Th sis psntation a0 nπx nπx f ( x) = + [ an cos + bn sin ] n = of a function
More informationSUPPLEMENTARY INFORMATION
SUPPLMNTARY INFORMATION. Dtmin th gat inducd bgap cai concntation. Th fild inducd bgap cai concntation in bilay gaphn a indpndntly vaid by contolling th both th top bottom displacmnt lctical filds D t
More informationCHAPTER 5 CIRCULAR MOTION
CHAPTER 5 CIRCULAR MOTION and GRAVITATION 5.1 CENTRIPETAL FORCE It is known that if a paticl mos with constant spd in a cicula path of adius, it acquis a cntiptal acclation du to th chang in th diction
More informationUsing Multiwavelength Spectroscopy. Alicia C. Garcia-Lopez
Hybid Modl fo Chaactization of Submicon Paticls Using Multiwavlngth Spctoscopy by Alicia C. Gacia-Lopz A disstation submittd in patial fulfillmnt of th quimnts fo th dg of Docto of Philosophy Dpatmnt of
More informationPolarized Transmittance-Reflectance Scatterometry Measurements of 2D Trench Dimensions on Phase-Shift Masks
Poaid Tansmittanc-Rctanc Scattomt Masumnts o D Tnch Dimnsions on Phas-Shit Mass John C. am, Aand Ga, Raa How, Stan Chn n& Tchnoog, nc., Santa Caa, CA 9554 Phsics Dpatmnt, Univsit o Caionia at Davis, CA
More informationQ Q N, V, e, Quantum Statistics for Ideal Gas and Black Body Radiation. The Canonical Ensemble
Quantum Statistics fo Idal Gas and Black Body Radiation Physics 436 Lctu #0 Th Canonical Ensmbl Ei Q Q N V p i 1 Q E i i Bos-Einstin Statistics Paticls with intg valu of spin... qi... q j...... q j...
More informationGAUSS PLANETARY EQUATIONS IN A NON-SINGULAR GRAVITATIONAL POTENTIAL
GAUSS PLANETARY EQUATIONS IN A NON-SINGULAR GRAVITATIONAL POTENTIAL Ioannis Iaklis Haanas * and Michal Hany# * Dpatmnt of Physics and Astonomy, Yok Univsity 34 A Pti Scinc Building Noth Yok, Ontaio, M3J-P3,
More informationThe geometric construction of Ewald sphere and Bragg condition:
The geometic constuction of Ewald sphee and Bagg condition: The constuction of Ewald sphee must be done such that the Bagg condition is satisfied. This can be done as follows: i) Daw a wave vecto k in
More informationInternational Journal of Scientific & Engineering Research, Volume 7, Issue 9, September ISSN
Intnational Jounal of cintific & Engining Rsach, Volum 7, Issu 9, ptmb-016 08 Analysis and Dsign of Pocklingotn s Equation fo any Abitay ufac fo Radiation Pavn Kuma Malik [1], Haish Pathasathy [], M P
More information1 Fundamental Solutions to the Wave Equation
1 Fundamental Solutions to the Wave Equation Physical insight in the sound geneation mechanism can be gained by consideing simple analytical solutions to the wave equation. One example is to conside acoustic
More informationWhile flying from hot to cold, or high to low, watch out below!
STANDARD ATMOSHERE Wil flying fom ot to cold, o ig to low, watc out blow! indicatd altitud actual altitud STANDARD ATMOSHERE indicatd altitud actual altitud STANDARD ATMOSHERE Wil flying fom ot to cold,
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 information(, ) which is a positively sloping curve showing (Y,r) for which the money market is in equilibrium. The P = (1.4)
ots lctu Th IS/LM modl fo an opn conomy is basd on a fixd pic lvl (vy sticky pics) and consists of a goods makt and a mony makt. Th goods makt is Y C+ I + G+ X εq (.) E SEK wh ε = is th al xchang at, E
More informationSTATISTICAL MECHANICS OF DIATOMIC GASES
Pof. D. I. ass Phys54 7 -Ma-8 Diatomic_Gas (Ashly H. Cat chapt 5) SAISICAL MECHAICS OF DIAOMIC GASES - Fo monatomic gas whos molculs hav th dgs of fdom of tanslatoy motion th intnal u 3 ngy and th spcific
More informationMultipole Radiation. February 29, The electromagnetic field of an isolated, oscillating source
Multipole Radiation Febuay 29, 26 The electomagnetic field of an isolated, oscillating souce Conside a localized, oscillating souce, located in othewise empty space. We know that the solution fo the vecto
More informationGRAVITATION 4) R. max. 2 ..(1) ...(2)
GAVITATION PVIOUS AMCT QUSTIONS NGINING. A body is pojctd vtically upwads fom th sufac of th ath with a vlocity qual to half th scap vlocity. If is th adius of th ath, maximum hight attaind by th body
More information* Meysam Mohammadnia Department of Nuclear Engineering, East Tehran Branch, Islamic Azad University, Tehran, Iran *Author for Correspondence
Indian Jouna o Fundanta and ppid Li Scincs ISSN: 65 Onin n Opn ccss, Onin Intnationa Jouna vaiab at www.cibtch.og/sp.d/js///js.ht Vo. S, pp. 7-/Mysa Rsach tic CQUISITION N NLYSIS OF FLUX N CURRENT COEFFICIENTS
More informationFree carriers in materials
Lctu / F cais in matials Mtals n ~ cm -3 Smiconductos n ~ 8... 9 cm -3 Insulatos n < 8 cm -3 φ isolatd atoms a >> a B a B.59-8 cm 3 ϕ ( Zq) q atom spacing a Lctu / "Two atoms two lvls" φ a T splitting
More informationLecture Principles of scattering and main concepts.
Lectue 15. Light catteing and aboption by atmopheic paticuate. Pat 1: Pincipe of catteing. Main concept: eementay wave, poaization, Stoke matix, and catteing phae function. Rayeigh catteing. Objective:
More informationDIELECTRICS MICROSCOPIC VIEW
HYS22 M_ DILCTRICS MICROSCOIC VIW DILCTRIC MATRIALS Th tm dilctic coms fom th Gk dia lctic, wh dia mans though, thus dilctic matials a thos in which a stady lctic fild can st up without causing an appcial
More informationPH672 WINTER Problem Set #1. Hint: The tight-binding band function for an fcc crystal is [ ] (a) The tight-binding Hamiltonian (8.
PH67 WINTER 5 Poblm St # Mad, hapt, poblm # 6 Hint: Th tight-binding band function fo an fcc cstal is ( U t cos( a / cos( a / cos( a / cos( a / cos( a / cos( a / ε [ ] (a Th tight-binding Hamiltonian (85
More informationCurrent Status of Orbit Determination methods in PMO
unt ttus of Obit Dtintion thods in PMO Dong Wi, hngyin ZHO, Xin Wng Pu Mountin Obsvtoy, HINEE DEMY OF IENE bstct tit obit dtintion OD thods hv vovd ot ov th st 5 ys in Pu Mountin Obsvtoy. This tic ovids
More informationPhysics 505 Electricity and Magnetism Fall 2003 Prof. G. Raithel. Problem Set 7 Maximal score: 25 Points. 1. Jackson, Problem Points.
Physics 505 Eecticity and Magnetism Fa 00 Pof. G. Raithe Pobem et 7 Maxima scoe: 5 Points. Jackson, Pobem 5. 6 Points Conside the i-th catesian component of the B-Fied, µ 0 I B(x) ˆx i ˆx i d (x x ) x
More informationAdvanced Quantum Mechanics
Advanced Quantum Mechanics Rajdeep Sensama sensama@theoy.tif.es.in Scatteing Theoy Ref : Sakuai, Moden Quantum Mechanics Tayo, Quantum Theoy of Non-Reativistic Coisions Landau and Lifshitz, Quantum Mechanics
More informationCollisionless Hall-MHD Modeling Near a Magnetic Null. D. J. Strozzi J. J. Ramos MIT Plasma Science and Fusion Center
Collisionlss Hall-MHD Modling Na a Magntic Null D. J. Stoi J. J. Ramos MIT Plasma Scinc and Fusion Cnt Collisionlss Magntic Rconnction Magntic connction fs to changs in th stuctu of magntic filds, bought
More information1.2 Partial Wave Analysis
February, 205 Lecture X.2 Partia Wave Anaysis We have described scattering in terms of an incoming pane wave, a momentum eigenet, and and outgoing spherica wave, aso with definite momentum. We now consider
More informationDifferential Kinematics
Lctu Diffntia Kinmatic Acknowgmnt : Pof. Ouama Khatib, Robotic Laboato, tanfo Univit, UA Pof. Ha Aaa, AI Laboato, MIT, UA Guiing Qution In obotic appication, not on th poition an ointation, but th vocit
More information6.Optical and electronic properties of Low
6.Optical and lctonic poptis of Low dinsional atials (I). Concpt of Engy Band. Bonding foation in H Molculs Lina cobination of atoic obital (LCAO) Schoding quation:(- i VionV) E find a,a s.t. E is in a
More information19 th WIEN2k Workshop Waseda University Tokyo Relativistic effects & Non-collinear magnetism. (WIEN2k / WIENncm)
9 th WIENk Wokshop Wasda Univsity Tokyo Rlativistic ffcts & Non-collina magntism WIENk / WIENncm) Xavi Rocquflt Institut ds Matéiaux Jan-RouxlUMR 65) Univsité d Nants, FRANCE 9 th WIENk Wokshop Wasda Univsity
More informationNEWTON S THEORY OF GRAVITY
NEWTON S THEOY OF GAVITY 3 Concptual Qustions 3.. Nwton s thid law tlls us that th focs a qual. Thy a also claly qual whn Nwton s law of gavity is xamind: F / = Gm m has th sam valu whth m = Eath and m
More informationCDS 101/110: Lecture 7.1 Loop Analysis of Feedback Systems
CDS 11/11: Lctu 7.1 Loop Analysis of Fdback Systms Novmb 7 216 Goals: Intoduc concpt of loop analysis Show how to comput closd loop stability fom opn loop poptis Dscib th Nyquist stability cition fo stability
More informationTotal Wave Function. e i. Wave function above sample is a plane wave: //incident beam
Total Wav Function Wav function abov sampl is a plan wav: r i kr //incidnt bam Wav function blow sampl is a collction of diffractd bams (and ): r i k r //transmittd bams k ks W nd to know th valus of th.
More informationA Study of Generalized Thermoelastic Interaction in an Infinite Fibre-Reinforced Anisotropic Plate Containing a Circular Hole
Vol. 9 0 ACTA PHYSICA POLONICA A No. 6 A Study of Gnalizd Thmolastic Intaction in an Infinit Fib-Rinfocd Anisotopic Plat Containing a Cicula Hol Ibahim A. Abbas a,b, and Abo-l-nou N. Abd-alla a,b a Dpatmnt
More informationdt d Chapter 30: 1-Faraday s Law of induction (induced EMF) Chapter 30: 1-Faraday s Law of induction (induced Electromotive Force)
Chaptr 3: 1-Faraday s aw of induction (inducd ctromotiv Forc) Variab (incrasing) Constant Variab (dcrasing) whn a magnt is movd nar a wir oop of ara A, currnt fows through that wir without any battris!
More informationFREQUENCY DETECTION METHOD BASED ON RECURSIVE DFT ALGORITHM
FREQUECY DETECTIO METHOD BAED O RECURIE ALGORITHM Katsuyasu akano*, Yutaka Ota*, Hioyuki Ukai*, Koichi akamua*, and Hidki Fujita** *Dpt. of ystms Managmnt and Engining, agoya Institut of Tchnology, Gokiso-cho,
More information5.61 Fall 2007 Lecture #2 page 1. The DEMISE of CLASSICAL PHYSICS
5.61 Fall 2007 Lctu #2 pag 1 Th DEMISE of CLASSICAL PHYSICS (a) Discovy of th Elcton In 1897 J.J. Thomson discovs th lcton and masus ( m ) (and inadvtntly invnts th cathod ay (TV) tub) Faaday (1860 s 1870
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 information1.2 Faraday s law A changing magnetic field induces an electric field. Their relation is given by:
Elctromagntic Induction. Lorntz forc on moving charg Point charg moving at vlocity v, F qv B () For a sction of lctric currnt I in a thin wir dl is Idl, th forc is df Idl B () Elctromotiv forc f s any
More informationθ θ φ EN2210: Continuum Mechanics Homework 2: Polar and Curvilinear Coordinates, Kinematics Solutions 1. The for the vector i , calculate:
EN0: Continm Mchanics Homwok : Pola and Cvilina Coodinats, Kinmatics Soltions School of Engining Bown Univsity x δ. Th fo th vcto i ij xx i j vi = and tnso S ij = + 5 = xk xk, calclat: a. Thi componnts
More informationImplementation of RCWA
Instucto D. Ramond Rumpf (915) 747 6958 cumpf@utep.edu EE 5337 Computational Electomagnetics Lectue # Implementation of RCWA Lectue These notes ma contain copighted mateial obtained unde fai use ules.
More informationShor s Algorithm. Motivation. Why build a classical computer? Why build a quantum computer? Quantum Algorithms. Overview. Shor s factoring algorithm
Motivation Sho s Algoith It appas that th univs in which w liv is govnd by quantu chanics Quantu infoation thoy givs us a nw avnu to study & tst quantu chanics Why do w want to build a quantu coput? Pt
More informationLecture 1. time, say t=0, to find the wavefunction at any subsequent time t. This can be carried out by
Lectue The Schödinge equation In quantum mechanics, the fundamenta quantity that descibes both the patice-ike and waveike chaacteistics of patices is wavefunction, Ψ(. The pobabiity of finding a patice
More information2. Background Material
S. Blair Sptmbr 3, 003 4. Background Matrial Th rst of this cours dals with th gnration, modulation, propagation, and ction of optical radiation. As such, bic background in lctromagntics and optics nds
More informationLecture 3.2: Cosets. Matthew Macauley. Department of Mathematical Sciences Clemson University
Lctu 3.2: Costs Matthw Macauly Dpatmnt o Mathmatical Scincs Clmson Univsity http://www.math.clmson.du/~macaul/ Math 4120, Modn Algba M. Macauly (Clmson) Lctu 3.2: Costs Math 4120, Modn Algba 1 / 11 Ovviw
More informationPhysics 202, Lecture 5. Today s Topics. Announcements: Homework #3 on WebAssign by tonight Due (with Homework #2) on 9/24, 10 PM
Physics 0, Lctu 5 Today s Topics nnouncmnts: Homwok #3 on Wbssign by tonight Du (with Homwok #) on 9/4, 10 PM Rviw: (Ch. 5Pat I) Elctic Potntial Engy, Elctic Potntial Elctic Potntial (Ch. 5Pat II) Elctic
More informationLecture 8 February 18, 2010
Sources of Eectromagnetic Fieds Lecture 8 February 18, 2010 We now start to discuss radiation in free space. We wi reorder the materia of Chapter 9, bringing sections 6 7 up front. We wi aso cover some
More informationSME 3033 FINITE ELEMENT METHOD. Bending of Prismatic Beams (Initial notes designed by Dr. Nazri Kamsah)
Bnding of Prismatic Bams (Initia nots dsignd by Dr. Nazri Kamsah) St I-bams usd in a roof construction. 5- Gnra Loading Conditions For our anaysis, w wi considr thr typs of oading, as iustratd bow. Not:
More informationRoger Pynn. Basic Introduction to Small Angle Scattering
by Roge Pynn Basic Intoduction to Small Angle Scatteing We Measue Neutons Scatteed fom a Sample Φ = numbe of incident neutons pe cm pe second σ = total numbe of neutons scatteed pe second / Φ dσ numbe
More informationJackson 3.3 Homework Problem Solution Dr. Christopher S. Baird University of Massachusetts Lowell
Jackson 3.3 Homewok Pobem Soution D. Chistophe S. Baid Univesity of Massachusetts Lowe POBLEM: A thin, fat, conducting, cicua disc of adius is ocated in the x-y pane with its cente at the oigin, and is
More informationPhysics 111. Lecture 38 (Walker: ) Phase Change Latent Heat. May 6, The Three Basic Phases of Matter. Solid Liquid Gas
Physics 111 Lctu 38 (Walk: 17.4-5) Phas Chang May 6, 2009 Lctu 38 1/26 Th Th Basic Phass of Matt Solid Liquid Gas Squnc of incasing molcul motion (and ngy) Lctu 38 2/26 If a liquid is put into a sald contain
More informationOverview. 1 Recall: continuous-time Markov chains. 2 Transient distribution. 3 Uniformization. 4 Strong and weak bisimulation
Rcall: continuous-tim Makov chains Modling and Vification of Pobabilistic Systms Joost-Pit Katon Lhstuhl fü Infomatik 2 Softwa Modling and Vification Goup http://movs.wth-aachn.d/taching/ws-89/movp8/ Dcmb
More informationFI 2201 Electromagnetism
F Eectomagnetism exane. skana, Ph.D. Physics of Magnetism an Photonics Reseach Goup Magnetostatics MGNET VETOR POTENTL, MULTPOLE EXPNSON Vecto Potentia Just as E pemitte us to intouce a scaa potentia V
More informationChapter 6: Polarization and Crystal Optics
Chaptr 6: Polarization and Crystal Optics * P6-1. Cascadd Wav Rtardrs. Show that two cascadd quartr-wav rtardrs with paralll fast axs ar quivalnt to a half-wav rtardr. What is th rsult if th fast axs ar
More informationJackson 4.7 Homework Problem Solution Dr. Christopher S. Baird University of Massachusetts Lowell
Jackson 4.7 Homewok obem Soution D. Chistophe S. Baid Univesity of Massachusetts Lowe ROBLEM: A ocaized distibution of chage has a chage density ρ()= 6 e sin θ (a) Make a mutipoe expansion of the potentia
More informationLossy Transmission Lines. EELE 461/561 Digital System Design. Module #7 Lossy Lines. Lossy Transmission Lines. Lossy Transmission Lines
Topics EEE 46/56 Digital Systm Dsign. Skin Ect. Dilctic oss Modul #7 ossy ins ossy ins - Whn w divd Tlgaphs Equations, w mad an assumption that th was no loss in th quivalnt cicuit modl i.., =, = - This
More informationElectron energy in crystal potential
Elctron nry in crystal potntial r r p c mc mc mc Expand: r r r mc mc mc r r p c mc mc mc r pc m c mc p m m m m r E E m m m r p E m r nr nr whr: E V mc E m c Wav quation Hamiltonian: Tim-Indpndnt Schrodinr
More informationECE Spring Prof. David R. Jackson ECE Dept. Notes 5
ECE 6345 Sping 15 Pof. David R. Jackson ECE Dept. Notes 5 1 Oveview This set of notes discusses impoved models of the pobe inductance of a coaxially-fed patch (accuate fo thicke substates). A paallel-plate
More informationAPP-IV Introduction to Astro-Particle Physics. Maarten de Jong
APP-IV Introduction to Astro-Particl Physics Maartn d Jong 1 cosmology in a nut shll Hubbl s law cosmic microwav background radiation abundancs of light lmnts (H, H, ) Hubbl s law (199) 1000 vlocity [km/s]
More informationFinite Element Method Modeling for Computational Electromagnetics Development of a Perfectly Matched Layer for Domain Termination
1 Finit Elmnt Mthod Modling o Computational Elctomagntics Dvlopmnt o a Pctly Matchd Lay o Domain Tmination Fist Smst Rpot Fall Smst 214 -Full pot- By Aaon Smull Tam Mmbs: Ana Manic Sanja Manic Ppad to
More informationSolution Set #3
05-733-009 Solution Set #3. Assume that the esolution limit of the eye is acminute. At what distance can the eye see a black cicle of diamete 6" on a white backgound? One acminute is, so conside a tiangle
More informationu 3 = u 3 (x 1, x 2, x 3 )
Lctur 23: Curvilinar Coordinats (RHB 8.0 It is oftn convnint to work with variabls othr than th Cartsian coordinats x i ( = x, y, z. For xampl in Lctur 5 w mt sphrical polar and cylindrical polar coordinats.
More information3. Electromagnetic Waves II
Lectue 3 - Electomagnetic Waves II 9 3. Electomagnetic Waves II Last time, we discussed the following. 1. The popagation of an EM wave though a macoscopic media: We discussed how the wave inteacts with
More information4.2 Design of Sections for Flexure
4. Dsign of Sctions for Flxur This sction covrs th following topics Prliminary Dsign Final Dsign for Typ 1 Mmbrs Spcial Cas Calculation of Momnt Dmand For simply supportd prstrssd bams, th maximum momnt
More informationChemistry 342 Spring, The Hydrogen Atom.
Th Hyrogn Ato. Th quation. Th first quation w want to sov is φ This quation is of faiiar for; rca that for th fr partic, w ha ψ x for which th soution is Sinc k ψ ψ(x) a cos kx a / k sin kx ± ix cos x
More informationFrictional effects, vortex spin-down
Chapt 4 Fictional ffcts, votx spin-down To undstand spin-up of a topical cyclon it is instuctiv to consid fist th spin-down poblm, which quis a considation of fictional ffcts. W xamin fist th ssntial dynamics
More informationMutual Inductance. If current i 1 is time varying, then the Φ B2 flux is varying and this induces an emf ε 2 in coil 2, the emf is
Mutua Inductance If we have a constant cuent i in coi, a constant magnetic fied is ceated and this poduces a constant magnetic fux in coi. Since the Φ B is constant, thee O induced cuent in coi. If cuent
More informationThe Great Wave Hokusai. LO: Recognize physical principles associated with terms in sonar equation.
Sona Equation: The Wave Equation The Geat Wave Hokusai LO: Recognize hysical inciles associated with tems in sona equation. the Punchline If density too high to esolve individual oganisms, then: E[enegy
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 informationAuxiliary Sources for the Near-to-Far-Field Transformation of Magnetic Near-Field Data
Auxiliay Soucs fo th Na-to-Fa-Fild Tansfomation of Magntic Na-Fild Data Vladimi Volski 1, Guy A. E. Vandnbosch 1, Davy Pissoot 1 ESAT-TELEMIC, KU Luvn, Luvn, Blgium, vladimi.volski@sat.kuluvn.b, guy.vandnbosch@sat.kuluvn.b
More informationStudy on the Classification and Stability of Industry-University- Research Symbiosis Phenomenon: Based on the Logistic Model
Jounal of Emging Tnds in Economics and Managmnt Scincs (JETEMS 3 (1: 116-1 Scholalink sach Institut Jounals, 1 (ISS: 141-74 Jounal jtms.scholalinksach.og of Emging Tnds Economics and Managmnt Scincs (JETEMS
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 informationEE 5337 Computational Electromagnetics (CEM) Method of Lines
11/30/017 Instucto D. Ramon Rumpf (915) 747 6958 cumpf@utp.u 5337 Computational lctomagntics (CM) Lctu #4 Mto of Lins Lctu 4 Ts nots ma contain copigt matial obtain un fai us uls. Distibution of ts matials
More information3.46 PHOTONIC MATERIALS AND DEVICES Lecture 10: LEDs and Optical Amplifiers
3.46 PHOTONIC MATERIALS AND DEVICES Lctu 0: LEDs and Optical Amplifis Lctu Rfncs:. Salh, M. Tich, Photonics, (John-Wily, Chapts 5-6. This lctu will viw how lctons and hols combin in smiconductos and nat
More information0WAVE PROPAGATION IN MATERIAL SPACE
0WAVE PROPAGATION IN MATERIAL SPACE All forms of EM nrgy shar thr fundamntal charactristics: 1) thy all tral at high locity 2) In traling, thy assum th proprtis of was 3) Thy radiat outward from a sourc
More informationChapter 5. Control of a Unified Voltage Controller. 5.1 Introduction
Chapt 5 Contol of a Unifid Voltag Contoll 5.1 Intoduction In Chapt 4, th Unifid Voltag Contoll, composd of two voltag-soucd convts, was mathmatically dscibd by dynamic quations. Th spac vcto tansfomation
More informationGeometrical Analysis of the Worm-Spiral Wheel Frontal Gear
Gomtical Analysis of th Wom-Spial Whl Fontal Ga SOFIA TOTOLICI, ICOLAE OACEA, VIRGIL TEODOR, GABRIEL FRUMUSAU Manufactuing Scinc and Engining Dpatmnt, Dunaa d Jos Univsity of Galati, Domnasca st., 8000,
More informationExtinction Ratio and Power Penalty
Application Not: HFAN-.. Rv.; 4/8 Extinction Ratio and ow nalty AVALABLE Backgound Extinction atio is an impotant paamt includd in th spcifications of most fib-optic tanscivs. h pupos of this application
More informationBasic properties of X- rays and neutrons
Basic popeties of X- ays and neutons Based on lectue notes of Sunil K. Sinha, UC San Diego, LANL J. Teixiea LLB Saclay G. Knelle, CBM Oléans/SOLEIL The photon also has wave and paticle popeties E=h! =hc/l=
More informationLecture 2: Frequency domain analysis, Phasors. Announcements
EECS 5 SPRING 24, ctu ctu 2: Fquncy domain analyi, Phao EECS 5 Fall 24, ctu 2 Announcmnt Th cou wb it i http://int.c.bkly.du/~5 Today dicuion ction will mt Th Wdnday dicuion ction will mo to Tuday, 5:-6:,
More informationDerivation of Electron-Electron Interaction Terms in the Multi-Electron Hamiltonian
Drivation of Elctron-Elctron Intraction Trms in th Multi-Elctron Hamiltonian Erica Smith Octobr 1, 010 1 Introduction Th Hamiltonian for a multi-lctron atom with n lctrons is drivd by Itoh (1965) by accounting
More informationBEHAVIOUR OF THE ELECTROMECHANICAL COUPLING FACTOR OF CYLINDER SHAPED PIEZOCERAMICS WITH DIFFERENT ASPECT RATIOS.
BEHAVIOUR OF THE ELECTROMECHANICAL COUPLING FACTOR OF CYLINER SHAPE PIEZOCERAMICS ITH IFFERENT ASPECT RATIOS. Pacs: 43.38.A Ia, Antonio; Lambti, Nicoa; Paaado, Massimo iatimnto di inggnia ttonica - Univsità
More informationECE theory of the Lamb shift in atomic hydrogen and helium
Gaphical Rsults fo Hydogn and Hlium 5 Jounal of Foundations of Physics and Chmisty,, vol (5) 5 534 ECE thoy of th Lamb shift in atomic hydogn and hlium MW Evans * and H Eckadt ** *Alpha Institut fo Advancd
More informationQ Q N, V, e, Quantum Statistics for Ideal Gas. The Canonical Ensemble 10/12/2009. Physics 4362, Lecture #19. Dr. Peter Kroll
Quantum Statistics fo Idal Gas Physics 436 Lctu #9 D. Pt Koll Assistant Pofsso Dpatmnt of Chmisty & Biochmisty Univsity of Txas Alington Will psnt a lctu ntitld: Squzing Matt and Pdicting w Compounds:
More informationSolutions. V in = ρ 0. r 2 + a r 2 + b, where a and b are constants. The potential at the center of the atom has to be finite, so a = 0. r 2 + b.
Solutions. Plum Pudding Model (a) Find the coesponding electostatic potential inside and outside the atom. Fo R The solution can be found by integating twice, 2 V in = ρ 0 ε 0. V in = ρ 0 6ε 0 2 + a 2
More information