Magnetism. 1 Paramagnetism. 2 Magnetic order. Introduction. Technology. Our first contact with magnetism. Plasma spectroscopy, Zeeman effect
|
|
|
- Stewart Leonard
- 6 years ago
- Views:
Transcription
1 agnetm Introducton magnetm nothng new... Paramagnetm agnetc order Our frt contact wth magnetm Technoogy agnetc Reonance Imagng Pama pectrocopy, Zeeman effect
2 Qu. What are the three ource of atomc magnetm and ort them by e.ucear pn moment?.eectron pn moment.orbta moment. What Len aw? Len aw (8: The nduced current produced n the conductor away fow n uch a drecton that the magnetc fed t produce w oppoe the change that produce t.?. How arge the magnetc fed you can generate wth: aa refrgerator magnet ban ron horehoe magnet ca uperconductng magnet. Whch matera react tronget on an apped magnetc fed? aargon ba co dfe Ferromagnetm of the eement Room-temperature magnet A other eement are: Paramagnetc or Damagnetc 8 dfferent type of magnetc matera Temperature dependence of magnetc uceptbty ( H, T = χ ( T H m T T C χ m (T Ferromagnetm or Ferrmagnetm Paramagnetm of ocaed eectron Antferromagnetm Paramagnetm of free eectron Damagnetm T ame and defnton H: magnetc fed / magnetc fed trength : magnetc nducton / magnetc fed In vacuum atera n magnetc fed H agnetaton agnetc uceptbty K m =reatve permeabty = H = ( H + = tot V = χ m H = K m H χ m = K m 9 atera Paramagnetc Iron oxde (FeO Iron amonum aum Uranum Patnum Tungten.8 Ceum. Aumnum. Lthum. agneum. Reatve o C χ m=k m- (x - Sodum. Oxygen ga.9 atera Damagnetc Ammona -. χ m=k m- (x - muth -. ercury -.9 Sver -. Carbon (damond -. Carbon (graphte -. Lead -.8 Sodum chorde -. Copper -. Water -.9 Paramagnetc uceptbty of ocaed eectron = χ(t H χ> parae to H Attractve force Lage T/hoog ved: Veradgd moment /T (T/K
3 ocaed eectron Champon n ocaaton: RE f he Some vaence he e deep n the atom have tte overap wth neghbor atom atomc orbta moment urvve band formaton Whch eectron of the eement are thee: Rare earth: Eectron confguraton f d Thu three open vaence he! Rada expectaton vaue of hydrogen orbta d tranton meta f Rare-earth meta f Eary actnde tte overap wth neghbor atom agnetc dpoe moment of atom wth eectron: Eectron ha pn and orbta moment contrbutng each to the magnetc dpoe moment orbt e = r p = m eh = = 9.x m /T = r x p = g pn g =. = ( (p (d Orbta moment n fed // ax, = = m (f m = = = Zeeman energy Orbta moment n magnetc fed. = m, = g Spn moment n fed // a = g m g =. h ± h Zeeman energy. = g m 8
4 Spn-orbt nteracton Spn-orbt pttng Spn orbt nteracton ead to pttng of eve Spn-orbt energy E pn orbt ucear reference frame = λ Z λ ~ n ( + ( + Eectron reference frame: rotatng proton produce magnetc fed (Reatvtc effect for tate wth quantum number n, : o pttng f = ( orbta Increae wth Z, decreae wth n, - mev for vaence he - ev for nner he ew egentate wth quantum number j=+ or j=- m j =j,j-, -j Labeng: j 9 Tota moment of vaence he n The tota magnetc moment the um of a magnetc dpoe moment ( L + S = hl = h Tota atomc orbta-moment = Tota atomc pn-moment hs = h = Fu he have no dpoe moment: n, np, nd, nf Party fed he have permanent dpoe moment Confguraton ~ ev - ev utpet pttng of np confguraton +Couomb nteracton Spectrocopc notaton: S+ L +Spn-orbt nteracton +magnetc fed (Zeeman pttng utpet tate Hund rue ground tate (here = Coupng cheme for addng orbta and pn anguar momenta. Rue Saunder or L-S coupng f pn-orbt nteracton weak egentate of the atom are ao egentate of L and S wth egenvaue L(L+ and S(S+. Add up a orbta moment Add up a pn moment L = S = Add thee together to tota atomc anguar moment =L+S = = Coupng cheme for addng orbta and pn anguar moment. j-j coupng f pn-orbt nteracton domnant Add up orbta and pn moment of each eectron = + Add thee together to = =. Intermedate coupng compcated no fxed rue
5 Hund rue for of ground tate Procedure for of the ground tate (L-S coupng:. axme S=Σ,. axme L =Σ,. = L-S for e than haf fed he L+S for more than haf fed he f ubhe exacty haf-fed, fed, L=, o = S exampe: d tranton meta: F the d orbta (=..... d S L # eectron Zeeman effect for tate wth tota moment Ground tate + tme degenerated: =-, -+, Spt n magnetc fed nto ubeve ΔE = g L - - H = = Spectrocopc pttng factor g Landee depend on L, S, and Spttng at = Tea n the order of mev Atom behave a f t ha effectve moment: eff =-g L P E =< H >= g g Lande P Lande L( L + S ( S + = ( + Effectve moment often caed m once we have,, we can get the maxmum component of the magnetc moment of the atom parae to the magnetc fed: Confguraton utpet + magnetc fed: Zeeman effect +Couomb nteracton +Spn-baan nteracton +magnetc fed (Zeeman pttng g, Landé pttng factor: pure orbta moton =, pure pn = Typcay ev Spttng typcay mev Here: = ground tate non-magnetc nget 8 = Temperature dependence ΔE = g L - - magnetc moment of ytem wth on at T determned by otmann tattc: g g exp( k = T = g exp( k T g (, T = g k T roun functon aturated moment /T (T/K 9 g (, T = g k T for not too ma T: Cure aw p χ m ( T = k T [ ( + ] p = glandee Effectve number of magneton Cure aw χ m (T T /T (T/K T
6 How we work Hund rue? Effectve number magneton 8 p = g f Landee [ ( + ] p_ p_mea # eectron 8 d p_ p_s p_mea # eectron p S = [ S( S + ] Paramagnetm of band eectron Up to now: ocaed eectron When vaence eectron form a band, orbta moment quenched Yet we ee a paramagnetc moment n meta Expaned by Wofgang Pau In d tranton meta deocaaton detroy orbta moment (quenchng Paramagnetm of free eectron ga Suceptbte are ma g ( ε F ΔE = Fed ft pn degeneracy Etmate: Δn = g ( ε ( χ( T = = g εf H Pau paramagnetm Temperature ndependent F a uceptbty (m kg - Room temperature uceptbte of frt eement Typca denty:. mo/cm oar uc. χ mo = - <<
Physics 2D Lecture Slides Lecture 30: Mar 12th
Course revew s schedued for Sunday 4 th March at 0am n WLH 005 There w be no Streamng vdeo for ths sesson, so p. attend Physcs D Lecture Sdes Lecture 30: Mar th Vvek Sharma UCSD Physcs d Φ + Φ = dφ m 0..
24. Atomic Spectra, Term Symbols and Hund s Rules
Page of 4. Atomc Spectra, Term Symbols and Hund s Rules Date: 5 October 00 Suggested Readng: Chapters 8-8 to 8- of the text. Introducton Electron confguratons, at least n the forms used n general chemstry
k p theory for bulk semiconductors
p theory for bu seconductors The attce perodc ndependent partce wave equaton s gven by p + V r + V p + δ H rψ ( r ) = εψ ( r ) (A) 4c In Eq. (A) V ( r ) s the effectve attce perodc potenta caused by the
5.03, Inorganic Chemistry Prof. Daniel G. Nocera Lecture 2 May 11: Ligand Field Theory
5.03, Inorganc Chemstry Prof. Danel G. Nocera Lecture May : Lgand Feld Theory The lgand feld problem s defned by the followng Hamltonan, h p Η = wth E n = KE = where = m m x y z h m Ze r hydrogen atom
VIII. Addition of Angular Momenta
VIII Addition of Anguar Momenta a Couped and Uncouped Bae When deaing with two different ource of anguar momentum, Ĵ and Ĵ, there are two obviou bae that one might chooe to work in The firt i caed the
Luigi Paolasini
Luigi Paolasini paolasini@esrf.fr LECTURE 2: LONELY ATOMS - Systems of electrons - Spin-orbit interaction and LS coupling - Fine structure - Hund s rules - Magnetic susceptibilities Reference books: -
Robert Eisberg Second edition CH 09 Multielectron atoms ground states and x-ray excitations
Quantum Physcs 量 理 Robert Esberg Second edton CH 09 Multelectron atoms ground states and x-ray exctatons 9-01 By gong through the procedure ndcated n the text, develop the tme-ndependent Schroednger equaton
CHAPTER 8 Atomic Physics
CHAPTER 8 Atomic Physics 8.1 Atomic Structure and the Periodic Table 8.2 Total Angular Momentum 8.3 Anomalous Zeeman Effect What distinguished Mendeleev was not only genius, but a passion for the elements.
Complex Atoms; The Exclusion Principle and the Periodic System
Complex Atoms; The Excluson Prncple and the Perodc System In order to understand the electron dstrbutons n atoms, another prncple s needed. Ths s the Paul excluson prncple: No two electrons n an atom can
Calculation of Tin Atomic Data and Plasma Properties
AN-ET-04/4 Cacuaton of Tn Atomc Data and Pasma Propertes prepared by Energy Technoogy Dvson Argonne Natona aboratory Argonne Natona aboratory s managed by The Unversty of Chcago for the U. S. Department
[WAVES] 1. Waves and wave forces. Definition of waves
![[WAVES] 1. Waves and wave forces. Definition of waves](/thumbs/94/120548750.jpg "[WAVES] 1. Waves and wave forces. Definition of waves")
1. Waves and forces Defnton of s In the smuatons on ong-crested s are consdered. The drecton of these s (μ) s defned as sketched beow n the goba co-ordnate sstem: North West East South The eevaton can
Supervised Learning. Neural Networks and Back-Propagation Learning. Credit Assignment Problem. Feedforward Network. Adaptive System.
Part 7: Neura Networ & earnng /2/05 Superved earnng Neura Networ and Bac-Propagaton earnng Produce dered output for tranng nput Generaze reaonaby & appropratey to other nput Good exampe: pattern recognton
HO 40 Solutions ( ) ˆ. j, and B v. F m x 10-3 kg = i + ( 4.19 x 10 4 m/s)ˆ. (( )ˆ i + ( 4.19 x 10 4 m/s )ˆ j ) ( 1.40 T )ˆ k.
.) m.8 x -3 g, q. x -8 C, ( 3. x 5 m/)ˆ, and (.85 T)ˆ The magnetc force : F q (. x -8 C) ( 3. x 5 m/)ˆ (.85 T)ˆ F.98 x -3 N F ma ( ˆ ˆ ) (.98 x -3 N) ˆ o a HO 4 Soluton F m (.98 x -3 N)ˆ.8 x -3 g.65 m.98
Phys 402: Raman Scattering. Spring Introduction: Brillouin and Raman spectroscopy. Raman scattering: how does it look like?
Phy 402: Raman Scatterng Sprng 2008 1 Introducton: Brlloun and Raman pectrocopy Inelatc lght catterng medated by the electronc polarzablty of the medum a materal or a molecule catter rradant lght from
Chapter 7 Four-Wave Mixing phenomena
Chapter 7 Four-Wave Mx phenomena We wll dcu n th chapter the general nonlnear optcal procee wth four nteract electromagnetc wave n a NLO medum. Frt note that FWM procee are allowed n all meda (nveron or
64-311/5: Atomic and Molecular Spectra
64-311-Questions.doc 64-311/5: Atomic and Molecular Spectra Dr T Reddish (Room 89-1 Essex Hall) SECTION 1: REVISION QUESTIONS FROM 64-310/14 ε ο = 8.854187817 x 10-1 Fm -1, h = 1.0545766 x 10-34 Js, e
Chapter 6 The Effect of the GPS Systematic Errors on Deformation Parameters
Chapter 6 The Effect of the GPS Sytematc Error on Deformaton Parameter 6.. General Beutler et al., (988) dd the frt comprehenve tudy on the GPS ytematc error. Baed on a geometrc approach and aumng a unform
Scattering of two identical particles in the center-of. of-mass frame. (b)
Lecture # November 5 Scatterng of two dentcal partcle Relatvtc Quantum Mechanc: The Klen-Gordon equaton Interpretaton of the Klen-Gordon equaton The Drac equaton Drac repreentaton for the matrce α and
( ) electron gives S = 1/2 and L = l 1
Practice Modern Physics II, W018, Set 1 Question 1 Energy Level Diagram of Boron ion B + For neutral B, Z = 5 (A) Draw the fine-structure diagram of B + that includes all n = 3 states Label the states
hole h vs. e configurations: l l for N > 2 l + 1 J = H as example of localization, delocalization, tunneling ikx k
Infinite 1-D Lattice CTDL, pages 1156-1168 37-1 LAST TIME: ( ) ( ) + N + 1 N hoe h vs. e configurations: for N > + 1 e rij unchanged ζ( NLS) ζ( NLS) [ ζn unchanged ] Hund s 3rd Rue (Lowest L - S term of
Spin. Introduction. Michael Fowler 11/26/06
Spn Mchael Fowler /6/6 Introducton The Stern Gerlach experment for the smplest possble atom, hydrogen n ts ground state, demonstrated unambguously that the component of the magnetc moment of the atom along
Lecture 6: Paramagnetism and elasticity
Lecture 6: Paramagnetism an easticity Appications o statistica methos Aims: pin paramagnetism: Paramagnetic sats Curie s Law. Entange poymers Roe o entropy in rubber easticity. February 07 Lecture 6 1
Pseudopotentials for ab initio electronic structure calculations
Workshop on Appcaton of Densty-Functona Theory n Condensed Matter Physcs, Surface Physcs, Chemstry, Engneerng and Boogy, Bern, 21-3 Juy 23 L4 Pseudopotentas for ab nto eectronc structure cacuatons Martn
Conservation of Angular Momentum = "Spin"
Page 1 of 6 Conservaton of Angular Momentum = "Spn" We can assgn a drecton to the angular velocty: drecton of = drecton of axs + rght hand rule (wth rght hand, curl fngers n drecton of rotaton, thumb ponts
( ) r! t. Equation (1.1) is the result of the following two definitions. First, the bracket is by definition a scalar product.
Chapter. Quantum Mechancs Notes: Most of the matera presented n ths chapter s taken from Cohen-Tannoudj, Du, and Laoë, Chap. 3, and from Bunker and Jensen 5), Chap... The Postuates of Quantum Mechancs..
22.51 Quantum Theory of Radiation Interactions
.51 Quantum Theory of Radaton Interactons Fna Exam - Soutons Tuesday December 15, 009 Probem 1 Harmonc oscator 0 ponts Consder an harmonc oscator descrbed by the Hamtonan H = ω(nˆ + ). Cacuate the evouton
and decompose in cycles of length two
Permutaton of Proceedng of the Natona Conference On Undergraduate Reearch (NCUR) 006 Domncan Unverty of Caforna San Rafae, Caforna Apr - 4, 007 that are gven by bnoma and decompoe n cyce of ength two Yeena
Magnetism in low dimensions from first principles. Atomic magnetism. Gustav Bihlmayer. Gustav Bihlmayer
IFF 10 p. 1 Magnetism in low dimensions from first principles Atomic magnetism Gustav Bihlmayer Institut für Festkörperforschung, Quantum Theory of Materials Gustav Bihlmayer Institut für Festkörperforschung
Multi-electron atoms (11) 2010 update Extend the H-atom picture to more than 1 electron: H-atom sol'n use for N-elect., assume product wavefct.
Mult-electron atoms (11) 2010 update Extend the H-atom pcture to more than 1 electron: VII 33 H-atom sol'n use for -elect., assume product wavefct. n ψ = φn l m where: ψ mult electron w/fct φ n l m one
So far: simple (planar) geometries
Physcs 06 ecture 5 Torque and Angular Momentum as Vectors SJ 7thEd.: Chap. to 3 Rotatonal quanttes as vectors Cross product Torque epressed as a vector Angular momentum defned Angular momentum as a vector
Chapter 6. Rotations and Tensors
Vector Spaces n Physcs 8/6/5 Chapter 6. Rotatons and ensors here s a speca knd of near transformaton whch s used to transforms coordnates from one set of axes to another set of axes (wth the same orgn).
Additional File 1 - Detailed explanation of the expression level CPD
Addtonal Fle - Detaled explanaton of the expreon level CPD A mentoned n the man text, the man CPD for the uterng model cont of two ndvdual factor: P( level gen P( level gen P ( level gen 2 (.).. CPD factor
6.1 Nondegenerate Perturbation Theory
6.1 Nondegenerate Perturbation Theory Analytic solutions to the Schrödinger equation have not been found for many interesting systems. Fortunately, it is often possible to find expressions which are analytic
Magnetic Materials. The inductor Φ B = LI (Q = CV) = L I = N Φ. Power = VI = LI. Energy = Power dt = LIdI = 1 LI 2 = 1 NΦ B capacitor CV 2
Magnetic Materials The inductor Φ B = LI (Q = CV) Φ B 1 B = L I E = (CGS) t t c t EdS = 1 ( BdS )= 1 Φ V EMF = N Φ B = L I t t c t B c t I V Φ B magnetic flux density V = L (recall I = C for the capacitor)
The Born-Oppenheimer Approximation
5.76 Lecture otes /16/94 Page 1 The Born-Oppenhemer Approxmaton For atoms we use SCF to defne 1e eff orbtals. Get V for each e n feld of e s n all other occuped () r orbtals. ψ ( r) = φ 1( r1) φ( r ) sngle
Many-Electron Atoms. Thornton and Rex, Ch. 8
Many-Electron Atoms Thornton and Rex, Ch. 8 In principle, can now solve Sch. Eqn for any atom. In practice, -> Complicated! Goal-- To explain properties of elements from principles of quantum theory (without
Week 11: Chapter 11. The Vector Product. The Vector Product Defined. The Vector Product and Torque. More About the Vector Product
The Vector Product Week 11: Chapter 11 Angular Momentum There are nstances where the product of two vectors s another vector Earler we saw where the product of two vectors was a scalar Ths was called the
1.1 Units, definitions and fundamental equations. How should we deal with B and H which are usually used for magnetic fields?
Advance Organizer: Chapter 1: Introduction to single magnetic moments: Magnetic dipoles Spin and orbital angular momenta Spin-orbit coupling Magnetic susceptibility, Magnetic dipoles in a magnetic field:
Angular Momentum and Fixed Axis Rotation. 8.01t Nov 10, 2004
Angular Momentum and Fxed Axs Rotaton 8.01t Nov 10, 2004 Dynamcs: Translatonal and Rotatonal Moton Translatonal Dynamcs Total Force Torque Angular Momentum about Dynamcs of Rotaton F ext Momentum of a
Chapter 4. Interaction of Many-Electron Atoms with Electromagnetic Radiation
Cpte 4. Intecton o ny-ecton Atos wt ectognetc Rdton Redng: Bnsden & ocn Cpte 9 ny-ecton Atos n n Fed Htonn V t A e p t A e p V t ea p H H Te-ndependent Htonn nt t H Intecton o te to wt te dton ed Te dependent
Physics 443, Solutions to PS 7
Physcs 443, Solutons to PS 7. Grffths 4.50 The snglet confguraton state s χ ) χ + χ χ χ + ) where that second equaton defnes the abbrevated notaton χ + and χ. S a ) S ) b χ â S )ˆb S ) χ In sphercal coordnates
Harmonic oscillator approximation
armonc ocllator approxmaton armonc ocllator approxmaton Euaton to be olved We are fndng a mnmum of the functon under the retrcton where W P, P,..., P, Q, Q,..., Q P, P,..., P, Q, Q,..., Q lnwgner functon
Time Independent Perturbation Theory Contd.
Time Independent Perturbation Theory Contd. A summary of the machinery for the Perturbation theory: H = H o + H p ; H 0 n >= E n n >; H Ψ n >= E n Ψ n > E n = E n + E n ; E n = < n H p n > + < m H p n
SOLVING THE KONDO PROBLEM FOR COMPLEX MESOSCOPIC SYSTEMS
SOLVING THE KONDO POBLEM FO COMPLEX MESOSCOPIC SYSTEMS V. DINU and M. ÞOLEA National Intitute of Material Phyic, Bucharet-Magurele P.O. Box MG-7, omania eceived February 21, 2005 Firt we preent the calculation
Interaction of matter with magnetic fields
LN07-1 Interaction of matter with magnetic fields All substances have magnetic properties, which can be determined by examining their behaviour in the presence of an external magnetic field, H. N S When
Electric and magnetic field sensor and integrator equations
Techncal Note - TN12 Electrc and magnetc feld enor and ntegrator uaton Bertrand Da, montena technology, 1728 oen, Swtzerland Table of content 1. Equaton of the derate electrc feld enor... 1 2. Integraton
2.4. Quantum Mechanical description of hydrogen atom
2.4. Quantum Mechanical description of hydrogen atom Atomic units Quantity Atomic unit SI Conversion Ang. mom. h [J s] h = 1, 05459 10 34 Js Mass m e [kg] m e = 9, 1094 10 31 kg Charge e [C] e = 1, 6022
Physics 607 Exam 1. ( ) = 1, Γ( z +1) = zγ( z) x n e x2 dx = 1. e x2
Physcs 607 Exam 1 Please be well-organzed, and show all sgnfcant steps clearly n all problems. You are graded on your wor, so please do not just wrte down answers wth no explanaton! Do all your wor on
SUPPLEMENTARY INFORMATION
do: 0.08/nature09 I. Resonant absorpton of XUV pulses n Kr + usng the reduced densty matrx approach The quantum beats nvestgated n ths paper are the result of nterference between two exctaton paths of
HW #3. 1. Spin Matrices. HW3-soln-improved.nb 1. We use the spin operators represented in the bases where S z is diagonal:
HW3-oln-mproved.nb HW #3. Spn Matrce We ue the pn operator repreented n the bae where S dagonal: S x = 880,
10/9/2003 PHY Lecture 11 1
Announcements 1. Physc Colloquum today --The Physcs and Analyss of Non-nvasve Optcal Imagng. Today s lecture Bref revew of momentum & collsons Example HW problems Introducton to rotatons Defnton of angular
5.76 Lecture #5 2/07/94 Page 1 of 10 pages. Lecture #5: Atoms: 1e and Alkali. centrifugal term ( +1)
5.76 Lecture #5 /07/94 Page 1 of 10 pages 1e Atoms: H, H + e, L +, etc. coupled and uncoupled bass sets Lecture #5: Atoms: 1e and Alkal centrfugal term (+1) r radal Schrödnger Equaton spn-orbt l s r 3
GREENBERGER- HORNE- ZEILINGER (GHZ) STATES IN QUANTUM DOT MOLECULE
GREENERGER- ORNE- ZEILINGER (GZ) STATES IN QUANTUM DOT MOLECULE A. SARMA and P. AWRYLAK QUANTUM TEORY GROUP INSTITUTE FOR MICROSTRUCTURAL SCIENCES NATIONAL RESEARC COUNCIL OF CANADA OTTAWA, KAOR,CANADA
Note on the Electron EDM
Note on the Electron EDM W R Johnson October 25, 2002 Abstract Ths s a note on the setup of an electron EDM calculaton and Schff s Theorem 1 Basc Relatons The well-known relatvstc nteracton of the electron
1.2 Rare earth atoms H Ψ=E Ψ, (1.2.1) where the non-relativistic Hamiltonian operator is. H = h2 2m. v ext (r i ) (1.2.
8 1. ELEMENTS OF RARE EARTH MAGNETISM 1.2 Rare earth atoms The starting point for the understanding of the magnetism of the rare earths is the description of the electronic states, particularly of the
More. The Zeeman Effect. Normal Zeeman Effect
More The Zeeman Effect As we mentioned in Chapter, the splitting of spectral lines when an atom is placed in an external magnetic field was looked for by Faraday, predicted on the basis of classical theory
Many-Electron Atoms. Thornton and Rex, Ch. 8
Many-Electron Atoms Thornton and Rex, Ch. 8 In principle, can now solve Sch. Eqn for any atom. In practice, -> Complicated! Goal-- To explain properties of elements from principles of quantum theory (without
Agenda Administrative Matters Atomic Physics Molecules
Fromm Institute for Lifeong Learning University of San Francisco Modern Physics for Frommies IV The Universe - Sma to Large Lecture 3 Agenda Administrative Matters Atomic Physics Moecues Administrative
A how to guide to second quantization method.
Phys. 67 (Graduate Quantum Mechancs Sprng 2009 Prof. Pu K. Lam. Verson 3 (4/3/2009 A how to gude to second quantzaton method. -> Second quantzaton s a mathematcal notaton desgned to handle dentcal partcle
Quantum Mechanics I Problem set No.1
Quantum Mechancs I Problem set No.1 Septembe0, 2017 1 The Least Acton Prncple The acton reads S = d t L(q, q) (1) accordng to the least (extremal) acton prncple, the varaton of acton s zero 0 = δs = t
Electronic Microstates & Term Symbols. Suggested reading: Shriver and Atkins, Chapter 20.3 or Douglas,
Lecture 4 Electronic Microstates & Term Symbols Suggested reading: Shriver and Atkins, Chapter 20.3 or Douglas, 1.4-1.5 Recap from last class: Quantum Numbers Four quantum numbers: n, l, m l, and m s Or,
Quantum spin system with on-site exchange in a magnetic field
Materals Scence-Poland, Vol. 25, No. 2, 2007 Quantum spn system wth on-ste exchange n a magnetc feld G. PAWŁOWSKI * Insttute of Physcs, Adam Mckewcz Unversty, 61-614 Poznań, ul. Umultowska 85, Poland We
Magnetic properties of the RbNd(WO 4 ) 2 single crystal. M.T.Borowiec 1*, E.Zubov 2, T.Zayarnyuk 1, M.Barański 1. Poland.
Magnetc propertes of the RbNd(WO 4 ) sngle crystal M.T.Borowec 1*, E.Zubov, T.Zayarnyuk 1, M.Barańsk 1. 1 Insttute of Physcs, Polsh Academy of Scences, al.lotnków 3/46, -668 Warsaw, Poland. A. A. Galkn
Lecture 10. Reading: Notes and Brennan Chapter 5
Lecture tatstcal Mechancs and Densty of tates Concepts Readng: otes and Brennan Chapter 5 Georga Tech C 645 - Dr. Alan Doolttle C 645 - Dr. Alan Doolttle Georga Tech How do electrons and holes populate
Nuclear Size and Density
Nucear Size and Density How does the imited range of the nucear force affect the size and density of the nucei? Assume a Vecro ba mode, each having radius r, voume V = 4/3π r 3. Then the voume of the entire
3. Stress-strain relationships of a composite layer
OM PO I O U P U N I V I Y O F W N ompostes ourse 8-9 Unversty of wente ng. &ech... tress-stran reatonshps of a composte ayer - Laurent Warnet & emo Aerman.. tress-stran reatonshps of a composte ayer Introducton
MAGNETISM MAGNETIC DIPOLES
MAGNETISM We now turn to magnetsm. Ths has actually been used for longer than electrcty. People were usng compasses to sal around the Medterranean Sea several hundred years BC. However t was not understood
Multielectron Atoms.
Multielectron Atoms. Chem 639. Spectroscopy. Spring 00 S.Smirnov Atomic Units Mass m e 1 9.109 10 31 kg Charge e 1.60 10 19 C Angular momentum 1 1.055 10 34 J s Permittivity 4 0 1 1.113 10 10 C J 1 m 1
A.1 Alkaline atoms in magnetic fields
164 Appendix the Kohn, virial and Bertrand s theorem, with an original approach. Annex A.4 summarizes elements of the elastic collisions theory required to address scattering problems. Eventually, annex
5.80 Small-Molecule Spectroscopy and Dynamics
MIT OpenCourseWare http://ocw.mit.edu 5.80 Small-Molecule Spectroscopy and Dynamics Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. 5.80 Lecture
Joel Broida UCSD Fall 2009 Phys 130B QM II. Homework Set 2 DO ALL WORK BY HAND IN OTHER WORDS, DON T USE MATHEMAT- ICA OR ANY CALCULATORS.
Joe Broida UCSD Fa 009 Phys 30B QM II Homework Set DO ALL WORK BY HAND IN OTHER WORDS, DON T USE MATHEMAT- ICA OR ANY CALCULATORS. You may need to use one or more of these: Y 0 0 = 4π Y 0 = 3 4π cos Y
( ) 1/ 2. ( P SO2 )( P O2 ) 1/ 2.
Chemstry 360 Dr. Jean M. Standard Problem Set 9 Solutons. The followng chemcal reacton converts sulfur doxde to sulfur troxde. SO ( g) + O ( g) SO 3 ( l). (a.) Wrte the expresson for K eq for ths reacton.
19 The Born-Oppenheimer Approximation
9 The Bon-Oppenheme Appoxmaton The full nonelatvstc Hamltonan fo a molecule s gven by (n a.u.) Ĥ = A M A A A, Z A + A + >j j (883) Lets ewte the Hamltonan to emphasze the goal as Ĥ = + A A A, >j j M A
Energy Level Energy Level Diagrams for Diagrams for Simple Hydrogen Model
Quantum Mechanics and Atomic Physics Lecture 20: Real Hydrogen Atom /Identical particles http://www.physics.rutgers.edu/ugrad/361 physics edu/ugrad/361 Prof. Sean Oh Last time Hydrogen atom: electron in
CHAPTER 9 LINEAR MOMENTUM, IMPULSE AND COLLISIONS
CHAPTER 9 LINEAR MOMENTUM, IMPULSE AND COLLISIONS 103 Phy 1 9.1 Lnear Momentum The prncple o energy conervaton can be ued to olve problem that are harder to olve jut ung Newton law. It ued to decrbe moton
Nuclear Shell Model. P461 - Nuclei II 1
Nuclear Shell Model Potential between nucleons can be studied by studying bound states (pn, ppn, pnn, ppnn) or by scattering cross sections: np -> np pp -> pp nd -> nd pd -> pd If had potential could solve
Week3, Chapter 4. Position and Displacement. Motion in Two Dimensions. Instantaneous Velocity. Average Velocity
Week3, Chapter 4 Moton n Two Dmensons Lecture Quz A partcle confned to moton along the x axs moves wth constant acceleraton from x =.0 m to x = 8.0 m durng a 1-s tme nterval. The velocty of the partcle
Atomic Spectra in Astrophysics
Atomic Spectra in Astrophysics Potsdam University : Wi 2016-17 : Dr. Lidia Oskinova lida@astro.physik.uni-potsdam.de Complex Atoms Non-relativistic Schrödinger Equation 02 [ N i=1 ( ) 2 2m e 2 i Ze2 4πǫ
5.80 Small-Molecule Spectroscopy and Dynamics
MIT OpenCourseWare http://ocw.mit.edu 5.80 Small-Molecule Spectroscopy and Dynamics Fall 008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. 5.80 Lecture
Chapter 6 Hidden Markov Models. Chaochun Wei Spring 2018
896 920 987 2006 Chapter 6 Hdden Markov Modes Chaochun We Sprng 208 Contents Readng materas Introducton to Hdden Markov Mode Markov chans Hdden Markov Modes Parameter estmaton for HMMs 2 Readng Rabner,
Physics 111. Exam #3. March 4, 2011
Phyic Exam #3 March 4, 20 Name Multiple Choice /6 Problem # /2 Problem #2 /2 Problem #3 /2 Problem #4 /2 Total /00 PartI:Multiple Choice:Circlethebetanwertoeachquetion.Anyothermark willnotbegivencredit.eachmultiple
Class: Life-Science Subject: Physics
Class: Lfe-Scence Subject: Physcs Frst year (6 pts): Graphc desgn of an energy exchange A partcle (B) of ass =g oves on an nclned plane of an nclned angle α = 3 relatve to the horzontal. We want to study
Search for Permanent Electric Dipole Moments of Francium Atom
Search for Permanent Electrc Dpole Moments of Francum Atom Yasuhro SAKEMI Research Center for Nuclear Physcs (RCNP) Osaka Unversty ECR Ion source + Beam lne to transport the heavy ons from AVF + Trap/Coolng
Problem #1. Known: All required parameters. Schematic: Find: Depth of freezing as function of time. Strategy:
BEE 3500 013 Prelm Soluton Problem #1 Known: All requred parameter. Schematc: Fnd: Depth of freezng a functon of tme. Strategy: In thee mplfed analy for freezng tme, a wa done n cla for a lab geometry,
12. The Hamilton-Jacobi Equation Michael Fowler
1. The Hamlton-Jacob Equaton Mchael Fowler Back to Confguraton Space We ve establshed that the acton, regarded as a functon of ts coordnate endponts and tme, satsfes ( ) ( ) S q, t / t+ H qpt,, = 0, and
Lecture 10 Support Vector Machines II
Lecture 10 Support Vector Machnes II 22 February 2016 Taylor B. Arnold Yale Statstcs STAT 365/665 1/28 Notes: Problem 3 s posted and due ths upcomng Frday There was an early bug n the fake-test data; fxed
Dirty frustrated magnets: order from disorder and disorder by disorder. Mike Zhitomirsky (CEA-Grenoble)
Drty frustrated magnets: order from dsorder and dsorder by dsorder Mke Zhtomrsky (CEA-Grenoble) Outlne collaborators: Order from dsorder V. Maryasn (UJF & CEA) vacances n trangular AF: lftng degeneracy
CHAPTER 2 MAGNETISM. 2.1 Magnetic materials
CHAPTER 2 MAGNETISM Magnetism plays a crucial role in the development of memories for mass storage, and in sensors to name a few. Spintronics is an integration of the magnetic material with semiconductor
Strong Markov property: Same assertion holds for stopping times τ.
Brownan moton Let X ={X t : t R + } be a real-valued stochastc process: a famlty of real random varables all defned on the same probablty space. Defne F t = nformaton avalable by observng the process up
Magnetism. Andreas Wacker Mathematical Physics Lund University
Magnetism Andreas Wacker Mathematical Physics Lund University Overview B=μ0(H+M) B: Magnetic field (T), satisfies div B=0 M: Magnetization (density of magnetic moments) H: H-field (A/m), satisfies curl
Root Locus Techniques
Root Locu Technque ELEC 32 Cloed-Loop Control The control nput u t ynthezed baed on the a pror knowledge of the ytem plant, the reference nput r t, and the error gnal, e t The control ytem meaure the output,
Rydberg atoms. Tobias Thiele
Rydberg atoms Tobias Thiee References T. Gaagher: Rydberg atoms Content Part : Rydberg atoms Part : A typica beam experiment Introduction hat is Rydberg? Rydberg atoms are (any) atoms in state with high
Vote today! Physics 122, Fall November (c) University of Rochester 1. Today in Physics 122: applications of induction
Phscs 1, Fall 01 6 Noember 01 Toda n Phscs 1: applcatons of nducton Generators, motors and back EMF Transformers Edd currents Vote toda! Hdropower generators on the Nagara Rer below the Falls. The ste
Estimation of a proportion under a certain two-stage sampling design
Etmaton of a roorton under a certan two-tage amng degn Danutė Kraavcatė nttute of athematc and nformatc Lthuana Stattc Lthuana Lthuana e-ma: raav@tmt Abtract The am of th aer to demontrate wth exame that
Validation of Lumped Mass Lateral Cantilever Shaft Vibration Simulation on Fixed-Pitch Vertical-Axis Ocean Current Turbine
Vadaton of Lumped Mass Latera Cantever Shaft Vbraton Smuaton on Fxed-Ptch Vertca-Axs Ocean Current urbne R. Hantoro 1, I. K. A. P. Utama, A. Susetyono, and Erwand 1 Abstract Research on the emergence of
8 Waves in Uniform Magnetized Media
8 Wave n Unform Magnetzed Meda 81 Suceptblte The frt order current can be wrtten j = j = q d 3 p v f 1 ( r, p, t) = ɛ 0 χ E For Maxwellan dtrbuton Y n (λ) = f 0 (v, v ) = 1 πvth exp (v V ) v th 1 πv th
Appendix for An Efficient Ascending-Bid Auction for Multiple Objects: Comment For Online Publication
Appendx for An Effcent Ascendng-Bd Aucton for Mutpe Objects: Comment For Onne Pubcaton Norak Okamoto The foowng counterexampe shows that sncere bddng by a bdders s not aways an ex post perfect equbrum
Part II: Statistical Physics
Chapter 6: Boltzmann Statistics SDSMT, Physics Fall Semester: Oct. - Dec., 2014 1 Introduction: Very brief 2 Boltzmann Factor Isolated System and System of Interest Boltzmann Factor The Partition Function
Introduction to Density Functional Theory. Jeremie Zaffran 2 nd year-msc. (Nanochemistry)
Introducton to Densty Functonal Theory Jereme Zaffran nd year-msc. (anochemstry) A- Hartree appromatons Born- Oppenhemer appromaton H H H e The goal of computatonal chemstry H e??? Let s remnd H e T e
Chapter 5. Magnetism and Matter
Chapter 5 Magnetism and Matter TABLE 5.1 THE DIPOLE ANALO Diamagnetic materials, when placed in a magnetic field, are magnetized in the direction opposite to the magnetic field; whereas paramagnetic and