Quantum Physics (quantum Theory, Quantum Mechanics)
Quantum physics(quantum theory, quantum mechanics)Part 21
Summary of 1st lecture classical physics explanation of black-body radiationfailed (ultraviolet catastrophe) Planck’s ad-hoc assumption of “energy quanta”of energy Equantum h , leads to a radiation spectrumwhich agrees with experiment. old generally accepted principle of “natura non facitsaltus” violated Other evidence for “quantization”: Photoelectric effect (Einstein: explained by “photon”hypothesis) Atomic spectra stability of atom Quantum theory born as attempt to address theseobservations2
Outline Recap Steps toward QM Matter waves Quantum mechanics Schrödinger equation derivation of SE from classical wave equation Heisenberg's matrix mechanics postulates of quantum mechanics examples of solutions to Schrödinger equation uncertainty (indeterminacy) principle3
Outline (2) quantum mechanics and atoms quantum mechanics of the hydrogen atom periodic table Compton scattering More on quantum mechanics postulates of quantum mechanics the problem of measurement probability amplitudes and quantuminterference the double slit experimento classical and QM interpretations4
Outline (3) Interpretation of quantum mechanics Discussion of double slit experiment wave particle duality, principle ofcomplementarity Copenhagen interpretation Other interpretations ? Atoms in magnetic field Stern Gerlach experiment Spin5
Steps towards QM Planck: Vibrating atoms have only certainenergies:o E hf or 2hf or 3hf, . Einstein: Energy is quantized in particles calledphotons:o E hf Bohr : Electrons in atoms can have only certainvalues of energy.RHE For hydrogen:n2RH 2.179 10 19 J 13.6 eV De Broglie: matter waves6
Momentum of a photon Relativistic relationship between a particle’smomentum and energy: E2 p2c2 m02c4 For massless (i.e. restmass 0) particlespropagating at the speed of light:E2 p2c2 , E pc For photon, E h momentum of photon h /c h/ , h/p “(moving) mass” of a photon:E mc2 m E/c2 h /c2(photon feels gravity)7
Matter waves Louis de Broglie (1925): any moving particle has wavelengthassociated with it: h/p example:o electron in atom has 10-10 m;o car (1000 kg) at 60mph has 10-38 m;o wave effects manifest themselves only in interaction with things ofsize comparable to wavelength we do not notice wave aspectof us and our cars. note: Bohr's quantization condition for angular momentum isidentical to requirement that integer number of electronwavelengths fit into circumference of orbit. experimental verification of de Broglie's matter waves:o beam of electrons scattered by crystal lattice shows diffractionpattern (crystal lattice acts like array of slits);experiment done by Davisson and Germer (1927)o Electron microscope8
QUANTUM MECHANICSnew kind of physics based on synthesis of dualnature of waves and particles; developed in1920's and 1930's. Schrödinger’s “wave mechanics”(Erwin Schrödinger, 1925)o Schrödinger equation is a differential equation formatter waves; basically a formulation of energyconservation.o its solution called “wave function”, usually denoted by ;o (x) 2 gives the probability of finding the particle at x;o applied to the hydrogen atom, the Schrödinger equationgives the same energy levels as those obtained from theBohr model;o the most probable orbits are those predicted by the Bohrmodel;o but probability instead of Newtonian certainty!9
Classical wave equation1 u u 2u ( x, t ) cos(2 t ) ( x)22v t x22 2 4 ( x) 022 xv22 4 v (x) 022 x ( x) A cos(2 x / )2210
Schrödinger equation Energy De Broglie Classical wave equ. de Brogliemv 2E V ( x), mv {2m[E-V ( x)]}1/22hh mv {2m[E-V ( x)]}1/2 2 4 2 2 2m[E-V ( x)] 2 ( x) 2 ( x) 022 x x 2 2 Schrödinger equation - 2m x 2 V ( x) ( x) E ( x)p2H ( x) ( V ( x)) ( x) E ( x)2m222p Energy operatorH K V ( x) V ( x) V ( x)22m2m x(Hamiltonian) p i Momentum operator x11
QM : Heisenberg Heisenberg’s “matrix mechanics”(Werner Heisenberg, 1925)o Matrix mechanics consists of an array of quantitieswhich when appropriately manipulated give theobserved frequencies and intensities of spectrallines.o Physical observables (e.g. momentum, position,.)are “operators” -- represented by matriceso The set of eigenvalues of the matrix representing anobservable is the set of all possible values that couldarise as outcomes of experiments conducted on asystem to measure the observable.o Shown to be equivalent to wave mechanics byErwin Schrödinger (1926)12
Postulates of Quantum Mechanics The state of a quantum mechanical system is completelyspecified by its wavefunction (or state function), x,t) For every classical observable there is a linear, Hermitianoperator in quantum mechanics In any measurement associated with an operator, the onlyvalues observed are eigenvalues of the operator,A ( x, t ) a ( x, t ) The average values of an observable is given by itsexpectation value, *A A d The wavefunction obeys the Schrödinger equationH E 2p V H “Hamiltonian” energy operator H K V 2m13
Potentials and Quantization (1) Consider a particle free to move in 1 dimension:pCase: ‘Free’ ParticlePotential V 0xSchrödinger Equation becomes: p2 p2p21 2H V ( p ) ( p) ( p ) mv ( p) E ( p),2m2m2 2m 0 2 p 2 2 ( ) k 2 x Energy ranges from 0 to infinity .not quantized,particle can have any arbitrary velocity14
Potentials and Quantization (2) position of the particle is constrained by apotential Case: “Particle in a Box” V 0 for 0 x L, V for all other x The possible position of particle is limited to thedimensions of the box, 0 to Linf.00xL15
Particle in a 1-Dimensional BoxSchrödinger equationH E , 2 2H V ( x)22m xoutside the box V ( x) , ( x) 0inside the box V ( x) 0,n 2 ( x) sin(kn x), kn l l 2 kn 2 2 2 2E n , n 1, .edu/ph130a/130 ticle in a box16
QM Solution for the particle in a box Like a standingwaveWhat does the energylook like? x n x 2sin L L Energy isquantizedEyy*yn2h 2E ,28mLn 1, 2,3,.17
Example: dye molecule dye molecule, the length of which can beconsidered as the length of the “box” to whichelectron is limited L 8Å 0.8 nm WavelengthNcorresponding totransition n 1 to n 2:N2h2h222 19 E n n 2 1 2.8x10J, initial 2 final2 8mL8m(8 Å ) 700 nm Observed value is 680 nm18
Uncertainty principle Uncertainty principle: (Werner Heisenberg, 1925)o it is impossible to simultaneously know a particle's exact position andmomentum p x ħ/2h 6.63 x 10-34 J s 4.14 x 10-15 eV·sħ h/(2 ) 1.055 x 10-34 J s 6.582 x 10-16 eV·s( p means “uncertainty” in our knowledgeof the momentum p)o also corresponding relation for energy and time: E t ħ/2 (but meaning here is different) note that there are many such uncertainty relations inquantum mechanics, for any pair of “incompatible”(non-commuting) observables (represented by “operators”) in general, P Q ½ [P,Q] o [P,Q] “commutator” of P and Q, PQ – QPo A denotes “expectation value”19
Example of Heisenberg Uncertainty: What is the uncertainty in velocity for an electronin a 1Å radius orbital x 1 Å 10-10m6.626 10 h p 4 x4 1 10 34 10Js m 5.27 10 21 kgm / s p 5.27 10 21kgm / s5m v 5.7 10sm9.11 10 31kg (Recall the speed of light is c 3 x108 m/s)20
Another Example: macroscopic object What is the uncertainty in position for a 80 kgstudent walking across campus at 1.3 m/s withan uncertainty in velocity of 1%. Dp m Dv (80kg)(0.013 m/s) 1.04 kg.m/s 346.626 10J .s h x 5.07 10 35 m4 p 4 1.04kgm / s Very small uncertainty so, we know whereyou are!21
from The God Particle by Leon Lederman:Leaving his wife at home, Schrödinger booked a villa inthe Swiss Alps for two weeks, taking with him hisnotebooks, two pearls, and an old Viennese girlfriend.Schrödinger's self-appointed mission was to save thepatched-up, creaky quantum theory of the time. TheViennese physicist placed a pearl in each ear to screenout any distracting noises. Then he placed thegirlfriend in bed for inspiration. Schrödinger had hiswork cut out for him. He had to create a new theoryand keep the lady happy. Fortunately, he was up to thetask. Heisenberg is out for a drive when he's stopped by atraffic cop. The cop says, "Do you know how fast youwere going?"Heisenberg says, "No, but I know where I am."22
Multi-electron Atoms Similar quantum numbers – but energies aredifferent. No two electrons can have the same set ofquantum numbers These two assumptions can be used to motivate(partially predict) the periodic table of theelements.23
Quantum Mechanics of the Hydrogen Atom En -13.6 eV/n2, n 1, 2, 3, (principal quantum number) Orbital quantum number l 0, 1, 2, n-1, o Angular Momentum, L (h/2 ) · l(l 1) Magnetic quantum number - l m l,(there are 2 l 1 possible values of m) Spin quantum number: ms ½24
Periodic table Pauli’s exclusion Principle: No two electrons in an atom can occupy thesame quantum state. When there are many electrons in an atom, theelectrons fill the lowest energy states first: lowest n lowest l lowest ml lowest ms this determines the electronic structure of atoms25
Summary so far electron was identified as particle emitted in photoelectric effect Einstein’s explanation of p.e. effect lends further credence to quantumidea Geiger, Marsden, Rutherford experiment disproves Thomson’s atommodel Planetary model of Rutherford not stable by classical electrodynamics Bohr atom model with de Broglie waves gives some qualitativeunderstanding of atoms, but only semiquantitative no explanation for missing transition lines angular momentum in ground state 0 (1 ) spin? Quantum mechanics: Schrödinger equation describes observations observables (position, momentum, angular momentum.)are operators which act on “state vectors” – wave functions26
Compton scattering 1 Scattering of X-rays on freeelectrons; Electrons supplied by graphite target; Outermost electrons in C looselybound; binding energy X ray energy electrons “quasi-free” Expectation from classicalelectrodynamics: radiation incident onfree electrons electrons oscillate atfrequency of incidentradiation emit lightof same frequency light scattered in alldirections electrons don’t gainenergy no change infrequency of light27
Compton scattering 2Compton (1923) measured intensity of scatteredX-rays from solid target, as function ofwavelength for different angles. Nobel prize1927.X-ray sourceCollimator(selects angle)Crystal(selectswavelength) TargetResult: peak in scattered radiation shifts to longerwavelength than source. Amount depends on θ (but notA.H. Compton, Phys. Rev. 22 409 (1923)on the target material).28
Compton scattering 3 Classical picture: oscillating electromagnetic field causesoscillations in positions of charged particles, which re-radiate in alldirections at same frequency as incident radiation. No change inwavelength of scattered light is expectedIncident light waveOscillating electronEmitted light wave Compton’s explanation: collisions between particles of light (X-rayphotons) and electrons in the materialBeforeAfterp scattered photonIncoming photonp θElectronpescattered electron29
Compton scattering 4BeforeAfterp scattered photonIncoming photonθp ElectronpeConservation of energyConservation of momentumh me c h p c m c22 2escattered electron 2 4 1/ 2ehˆp i p p e From this derive change in wavelength: h 1 cos me c c 1 cos 0h c Compton wavelength 2.4 10 12 mme c30
Compton scattering 5 unshifted peaks come fromcollision between the X-rayphoton and the nucleus of theatom ’ - (h/mNc)(1 - cos ) 0since mN me31
Postulates of Quantum Mechanics The state of a quantum mechanical system is completelyspecified by its wavefunction, x,t) For every classical observable there is a linear, Hermitianoperator in quantum mechanics In any measurement associated with an operator, the onlyvalues observed are eigenvalues of the operator,A ( x, t ) a ( x, t ) The average value of an observable is given by itsexpectation value, *A A d The wavefunction obeys the Schrödinger equationH E 2p V H “Hamiltonian” energy operator H K V 2m32
measurement (1) Measurement involves interaction with the system whichis subject to the measurement process Measurements always have “errors”, uncertainties, dueto: Imperfections of measuring equipment/process uncertain data System subject to random outside influences Measurement result with quoted uncertainty is really aprobabilistic statement: X x x really meansP ( X [ x x , x x ]) 0.68,P ( X [ x 2 x , x 2 x ]) 0.95 (assuming “gaussian errors”)33
Measurement (2) Any measurement disturbs the system will be in adifferent state from the one it was in before themeasurement Examples: Temperature measurement: thermometer gets into thermalequilibrium with measured system in- (or out-)flux of thermalenergy temperature changed Measure position of object – have to shine light onto it to see it,light photons transfer momentum to measured object Influence of measurement process, as well as randomoutside influences (non-isolation) can more easily beminimized for big (high mass) system expect physics of small systems to be moreprobabilistic34
Measurement (3) “Heisenberg microscope”: Try to measure position of atiny particle – image particlewith a microscopeUncertainty of particleposition angular resolutionof microscope 1.22 /D,where wavelength of usedlight, D diameter of objectivelensTo optimize positionresolution, need smallwavelength and large Dp h/ , energetic photonsneed to be scattered offparticle under large angles momentum of particlechanged Requirement fro precisemeasurement ofposition significant jolts toparticle uncertainty ofmomentum35
Measurement (4) Scientific statement about a measurement is a prediction: “momentum of this electron is 3 0.02 GeV/c” means: ifyou measure p, you will obtain (with 95% confidence)a value between 3-0.04 and 3 0.04 GeV/c ideal measurement: is reproducible Subsequent measurement of the same quantity willyield the same result brings the system into a special state that has theproperty of being unaffected by a further measurementof the same type36
Measurement (5): Quantum states Existence of quantum states is one of thepostulates of QM Any system has quantum states in which the outcomeof a measurement is certain. These states are unrealizable abstractions, butimportant Examples:o E1 the state in which a measurement of the system’senergy will certainly return the value E1o p the state in which a measurement of the system’smomentum will certainly return the value po x state for which measurement of position will givevalue x37
Measurement (6): Process of measurement “Generic” state : Results of measurement of momentum, position,.uncertain At best can give probability P(E) that energy will be E,P(p) that momentum will be p,. reproducibilty: after having measured energy withvalue E, repetition of energy measurement should giveagain same value E act of measuring energy jogged system from state into a different special state E energ. meas. E with prob. P(E) mom. meas. p with prob. P(p) p mom. meas. p with certainty Special states are idealizations38
Measurement (7) in general, different dynamical quantities (e.g.energy, position, momentum, etc.) areassociated with different special states. If you arecertain about the outcome of a measurement ofe.g. position, you cannot be certain about theoutcome of a measurement of momentum, orenergy dynamical quantities such as position or energyshould be considered as questions we can ask(by making a measurement) rather than intrinsicproperties of the system.39
Measurement (8) Outcomes of measurements are in generaluncertain; the most we can do is compute theprobability with which the various possibleoutcomes will arise QM more complicated than classical mechanics: Classical mechanics: predict values of x, p,. QM: need to compute probability distributionsP (x), P(p)40
Measurement (9) In classical mechanics, we simply compute expectationvalues of the quantum mechanical probabilitydistributions If probability distribution is very sharply peaked andnarrow around its expectation valuex xP ( x)d 3 x, enough to know the value of x , since probability ofmeasuring value significantly different from x isnegligibly small Classical mechanics physics of expectation values,provides complete predictions when underlying quantumprobability distributions are very narrow41
Probability amplitudes Probability used in many branches of science In QM, probabilities are calculated as modulussquared of a complex amplitude: P A 2 AA* Consider process that can happen in twodifferent ways, by two mutually exclusive routes,S or T The probability amplitude for it to happen by oneor the other route : A( S or T ) A( S ) A(T )instead of P( S or T ) P( S ) P(T ) This leads to “quantum mechanical interference”,gives rise to phenomena that have no analoguein classical physics42
Quantum interference Two routes, S, T for process Probability that event happens regardless ofroute: P( S or T ) A( S or T ) 2 A(S) A(T ) 2 A(S) 2 A( S ) A* (T ) A* ( S ) A(T ) A(T ) 2 P ( S ) P (T ) 2Re( A( S ) A* (T )) i.e. probability of event happening is not just sumof probabilities for each possible route, but thereis an additional term – “interference term” Term has no counterpart in standard probabilitytheory; depends on phases of probabilityamplitudes43
WAVE-PARTICLE DUALITY OF LIGHT Einstein (1924) : “There are therefore now two theories of light,both indispensable, and without any logical connection.” evidence for wave-nature of light: diffraction interference evidence for particle-nature of light: photoelectric effect Compton effect Light exhibits diffraction and interference phenomena that are onlyexplicable in terms of wave properties Light is always detected as packets (photons); we never observehalf a photon Number of photons proportional to energy density (i.e. to square ofelectromagnetic field strength)44
double slit experiment Originally performed by Young(1801) to demonstrate the wavenature of light. Has now beendone with electrons, neutrons, Heatoms, Classical physics expectation: twopeaks for particles, interferencepattern for wavesydθd sin D45
Fringe spacing in double slit experimentMaxima when:d sin n D d use small angle approximation n d dydθd sin Position on screen: separationbetween adjacentmaxima:y D tan D y D D D y d46
Double slit experiment -- interpretation classical: two slits are coherent sources of light interference due to superposition of secondary waves onscreen intensity minima and maxima governed by optical pathdifferences light intensity I A2, A total amplitude amplitude A at a point on the screenA2 A12 A22 2A1 A2 cosφ, φ phase differencebetween A1 and A2 at the point maxima for φ 2nπ minima for φ (2n 1)π φ depends on optical path difference δ: φ 2πδ/ interference only for coherent light sources; For two independent light sources: no interference sincenot coherent (random phase differences)47
Double slit experiment: low intensity Taylor’s experiment (1908): double slit experiment with verydim light: interference pattern emerged after waiting for fewweeks interference cannot be due to interaction between photons, i.e.cannot be outcome of destructive or constructive combinationof photons interference pattern is due to some inherent property ofeach photon – it “interferes with itself” while passing fromsource to screen photons don’t “split” – light detectors always show signals ofsame intensity slits open alternatingly: get two overlapping single-slitdiffraction patterns – no two-slit interference add detector to determine through which slit photon goes: no interference interference pattern only appears when experiment providesno means of determining through which slit photon passes mlhttp://abyss.uoregon.edu/ js/21st century ipedia.org/wiki/Double-slit experimenthttp://grad.physics.sunysb.edu/ amarch/48
double slit experiment with very low intensity ,i.e. one photon or atom at a time:get still interference pattern if we wait longenough49
Double slit experiment – QM interpretation patterns on screen are result of distribution of photons no way of anticipating where particular photon willstrike impossible to tell which path photon took – cannotassign specific trajectory to photon cannot suppose that half went through one slit andhalf through other can only predict how photons will be distributed onscreen (or over detector(s)) interference and diffraction are statistical phenomenaassociated with probability that, in a givenexperimental setup, a photon will strike a certain point high probability bright fringes low probability dark fringes50
Double slit expt. -- wave vs quantumwave theoryquantum theory pattern of fringes: Intensity bands due tovariations in square ofamplitude, A2, ofresultant wave on eachpoint on screen role of the slits: to provide two coherent sources of thesecondary waves thatinterfere on the screenpattern of fringes: Intensity bands due tovariations inprobability, P, of aphoton striking pointson screenrole of the slits: to present twopotential routes bywhich photon can passfrom source to screen51
double slit expt., wave function light intensity at a point on screen I depends on number ofphotons striking the pointnumber of photons probability P of finding photon there, i.eI P ψ 2, ψ wave function probability to find photon at a point on the screen :P ψ 2 ψ1 ψ2 2 ψ1 2 ψ2 2 2 ψ1 ψ2 cosφ; 2 ψ1 ψ2 cosφ is “interference term”; factor cosφ due to factthat ψs are complex functions wave function changes when experimental setup is changedo by opening only one slit at a timeo by adding detector to determine which path photon tooko by introducing anything which makes paths distinguishable52
Waves or Particles? Young’s double-slitdiffraction experimentdemonstrates the waveproperty of light. However, dimming thelight results in singleflashes on the screenrepresentative ofparticles.53
Electron Double-Slit Experiment C. Jönsson (Tübingen,Germany, 1961 very narrow slits relatively large distancesbetween the slits and theobservation screen. double-slitinterference effects forelectrons experiment demonstratesthat precisely the samebehavior occurs for both light(waves) and electrons(particles).54
Results on matter wave interferenceNeutrons, A Zeilinger etal. Reviews of ModernPhysics 60 1067-1073(1988)He atoms: O Carnal and J MlynekPhysical Review Letters 66 26892692 (1991)C60 molecules: MArndt et al. Nature401, 680-682(1999)With multiple-slitgratingFringe visibilitydecreases asmolecules areheated. L.Hackermülleret al. , Nature427 711-714(2004)Without gratingInterference patterns can not be explained classically - clear demonstration of matter waves55
Double slit experiment -- interpretation classical: two slits are coherent sources of light interference due to superposition of secondary waves onscreen intensity minima and maxima governed by optical pathdifferences light intensity I A2, A total amplitude amplitude A at a point on the screenA2 A12 A22 2A1 A2 cosφ, φ phase differencebetween A1 and A2 at the point maxima for φ 2nπ minima for φ (2n 1)π φ depends on optical path difference δ: φ 2πδ/ interference only for coherent light sources; For two independent light sources: no interference sincenot coherent (random phase differences)56
Which slit? Try to determine which slit the electron went through. Shine light on the double slit and observe with a microscope. After theelectron passes through one of the slits, light bounces off it; observing thereflected light, we determine which slit the electron went through. photon momentum electron momentum :Need ph d todistinguish the slits.Diffraction is significant onlywhen the aperture is thewavelength of the wave. momentum of the photons used to determine which slit the electron wentthrough momentum of the electron itself changes the direction of theelectron! The attempt to identify which slit the electron passes throughchanges the diffraction pattern!57
Discussion/interpretation of double slit experiment Reduce flux of particles arriving at the slits so that only oneparticle arrives at a time. -- still interference fringes observed! Wave-behavior can be shown by a single atom or photon. Each particle goes through both slits at once. A matter wave can interfere with itself. Wavelength of matter wave unconnected to any internal size ofparticle -- determined by the momentum If we try to find out which slit the particle goes through theinterference pattern vanishes! We cannot see the wave and particle nature at the same time. If we know which path the particle takes, we lose the fringes .Richard Feynman about two-slit experiment: “ a phenomenon which isimpossible, absolutely impossible, to explain in any classical way, and whichhas in it the heart of quantum mechanics. In reality it contains the onlymystery.”58
Wave – particle - duality So, everything is both a particle and a wave -disturbing!? “Solution”: Bohr’s Principle of Complementarity: It is not possible to describe physical observablessimultaneously in terms of both particles andwaves Physical observables:o quantities that can be experimentally measured. (e.g.position, velocity, momentum, and energy.)o in any given instance we must use either the particledescription or the wave description When we’re trying to measure particle properties,things behave like particles; when we’re not, theybehave like waves.59
Probability, Wave Functions, and theCopenhagen Interpretation Particles are also waves -- described by wave function The wave function determines the probability of findinga particle at a particular position in space at a giventime. The total probability of finding the particle is 1. Forcingthis condition on the wave function is callednormalization.60
The Copenhagen Interpretation Bohr’s interpretation of the wave function consisted ofthree principles: Born’s statistical interpretation, based on probabilitiesdetermined by the wave function Heisenberg’s uncertainty principle Bohr’s complementarity principle Together these three concepts form a logical interpretation of thephysical meaning of quantum theory. In the Copenhageninterpretation, physics describes only the results ofmeasurements. correspondence principle: results predicted by quantum physics must be identical tothose predicted by classical physics in those situations whereclassical physics corresponds to the experimental facts61
Atoms in magnetic field orbiting electron behaves like current loop magnetic moment μ current x area interaction energy μ·B (both vectors!) μ·B loop current -ev/(2πr) angular momentum L mvr magnetic moment - μB L/ħμB e ħ/2me “Bohr magneton” interaction energyn m μB BzA(m z –comp of L) LI re 62
Splitting of atomic energy levelsB 0B 0m 1m 0m -1(2l 1) states with sameenergy: m -l, lB 0: (2l 1) states withdistinct energiesPredictions: should always get an odd number oflevels. An s state (such as the ground state ofhydrogen, n 1, l 0, m 0) should not be split.(Hence the name“magnetic quantumnumber” for m.)Splitting was observed by Zeeman63
Stern - Gerlach experiment - 1 magnetic dipole moment associated with angular momentummagnetic dipole moment of atoms and quantization of angularmomentum direction anticipated from Bohr-Sommerfeld atommodelmagnetic dipole in uniform field magnetic field feels torque, butno net forcein non-uniform field there will be net force deflectionextent of deflection depends on non-uniformity of field particle’s magnetic dipole moment orientation of dipole moment relative tomag. fieldPredictions: Beam should split into an odd number ofparts (2l 1) A beam of atoms in an s state(e.g. the ground state of hydrogen,n 1, l 0, m 0) should not be split.SN 64
Stern-Gerlach experiment (1921)zMagnetOvenNx0Ag beamSAg-vaporAgcollim.N BAg beamS B B z z eznonuniform# Ag atomsscreenB 0B b0B 2bz65
Stern-Gerlach experiment - 3 beam of Ag atoms (with electron in s-state(l 0)) in non-uniform magnetic field force on atoms: F z· Bz/ z results show two groups of atoms,deflected in opposite directions, withmagnetic moments z B Conundrum: classical physics would predict acontinuous distribution of μ quantum mechanics à la BohrSommerfeld predicts an odd number (2ℓ 1) of groups, i.e. just one for an s state66
The concept of spin Stern-Gerlach results cannot be explained byinteraction of magnetic moment from orbital angularmomentum must be due to some additional internal source ofangular momentum that does not require motion ofthe electron. internal angular momentum of electron (“spin”) wassuggested in 1925 by Goudsmit and Uhlenbeckbuilding on an idea of Pauli. Spin is a
QUANTUM MECHANICS new kind of physics based on synthesis of dual nature of waves and particles; developed in 1920's and 1930's. Schrödinger's "wave mechanics" (Erwin Schrödinger, 1925) o Schrödinger equation is a differential equation for matter waves; basically a formulation of energy conservation.
Physics 20 General College Physics (PHYS 104). Camosun College Physics 20 General Elementary Physics (PHYS 20). Medicine Hat College Physics 20 Physics (ASP 114). NAIT Physics 20 Radiology (Z-HO9 A408). Red River College Physics 20 Physics (PHYS 184). Saskatchewan Polytechnic (SIAST) Physics 20 Physics (PHYS 184). Physics (PHYS 182).
Chapter 2 - Quantum Theory At the end of this chapter – the class will: Have basic concepts of quantum physical phenomena and a rudimentary working knowledge of quantum physics Have some familiarity with quantum mechanics and its application to atomic theory Quantization of energy; energy levels Quantum states, quantum number Implication on band theory
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terpretation of quantum physics. It gives new foundations that connect all of quantum physics (including quantum mechanics, statistical mechanics, quantum field theory and their applications) to experiment. Quantum physics, as it is used in practice, does much more than predicting probabili
Physics is a progressive subject and it is impossible to learn about Quantum Physics without a good grounding in classical physics, i.e. the physics that was understood by the end of the nineteenth century, before the discovery of Quantum Theory. Quantum Theory essentially deals with the fact that everything which can transmit energy behaves
Rae, Alastair I. M. Quantum physics: illusion or reality? 1. Quantum theory I. Title 530.1’2 QC174.12 Library of Congress Cataloguing in Publication data Rae, Alastair I. M. Quantum physics: illusion or reality? Bibliography Includes index. 1. Quantum theory. 2. Physics – Philosophy. I. Title. QC174.12.R335 1985 530.1’2 85 – 13256
Advanced Placement Physics 1 and Physics 2 are offered at Fredericton High School in a unique configuration over three 90 h courses. (Previously Physics 111, Physics 121 and AP Physics B 120; will now be called Physics 111, Physics 121 and AP Physics 2 120). The content for AP Physics 1 is divided
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