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# MODERN PHYSICS PHYS 301

ISU

GPA 3.6

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This 56 page Class Notes was uploaded by Jonatan Hartmann on Monday October 12, 2015. The Class Notes belongs to PHYS 301 at Idaho State University taught by Staff in Fall. Since its upload, it has received 27 views. For similar materials see /class/222185/phys-301-idaho-state-university in Physics 2 at Idaho State University.

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Date Created: 10/12/15

Modern Physics Fall 2008 Dr Starovoitova Lecture 2 1 SPINNlNG mummws Em 1mm nous TH PW 0 New mmuw SWING T5 SPIN 39I39Hl TINIEST BIT mummums 11 NIGHT Plme mm mm GIVING M A LITTLE MORE 1m HERE WIN YOU Review Lecture 20 Hydrogen wavefunction ground state 100 D5 R1s 146 Hydrogen wave function 200 D m m an m an r 4 R2sl A 2 e 2 a3 Hydrogen wavefunetions 2 10 21 1 etc functions of angle as well as r 211 Spin angular momentum ELECTRON ORBIT PRogou Sax JSL 39 7m L h 1 1 339 External S h SS 1 B mggnelmelu quotquotquotquotquot J I E L2 mlh I mquotfi393 f 52 m gt 203 Quantum numbers n Principle quantum number I Angular quantum number m Magnetic quantum number 0 5 Spin quantum number Ground state n 1 I 0 m0 n1 gt25tates Szilz n2 gt8states 2 First excited state n 2 D egener acy 2quot Z 0 l m 0 m 0i1 2 1 3 Magnetic moment W jaz yBjsm d yBcos U W uBcos Patenna energy 4 9 3 0 E LII C U 4 Z 3 j x 3 L3 m HK Ti IMquot T39 l I x 5 lt39 Egg y 2 1 3 Magnetic moment E i T 27W 6V 2 evr 39 7W a 27W 2 L mvr 2m i Z Gyromagnetic ratio 2m 214 Spin magnetic moment 6 gt L 2me 6 m e int orb spin 2 e In 1925 Samuel Goudsmit and George Uhlenbeck put forward the proposal of electron spin They suggested that electrons rotate about an aXis and as they are charged set up a magnetic field 2 l 5 Zeeman effect No Magnetic Field Magnetic Field present The Zeeman effect is splitting of atomic energy levels into a ml 1 larger number of levels when I1 mi0 m 1 magnetic fields are present the I Am 1 Amt 1 reSulting spectral lines are also Ami 0 split The pattern and amount of splitting indicate the strength I ID of the magnetic field Spectrum without Spectrum with magnetic magnetic eld eld present 2 1 5 Zeeman effect The Zeeman effect is used to study magnetic phenomena 0n the surface of the Sun 2 l 5 Zeeman effect He atom uspin I 0 singlet states One of the e has zero orbital angular momentum Thus the total magnetic moment is e L 2me Magnetic field off E0 Magnetic field on E0AE 2 1 5 Zeeman effect ig3 927gtlt10 24Am2 2me AE uBmB 2 1 5 Zeeman effect JMagne cfmhio EEki52ll degenerate z l0mOaLZO L l1am0i1LzOih L I 2 a m Oi1i2 a L2 Oihi2h 2 l 5 Zeeman effect Magnetic field on E0 changes by z different amount for each leVel thus destroying the degeneracy and we see splitting I 2 a m 012 a L2 Oihi2h Bfield off Bfield on 2 1 I HBB 0 E0 1 2 m 21012 33333 216 The anomalous Zeeman effect Now assume uspin 95 0 but uorb 0 8 u 3 me a a 6 AE u B S B me P Bfield off Bfield on S2 2 m 4L S eh AEzi BzinB lt ZHBB 2me ms 12 12 ms 12 216 The anomalous Zeeman effect The Zeeman effect The normal Zeeman effect The anomalous Zeeman effect Iuspm 0 gt gt spin 397 O Iuspin 397 0 Iuorb i O tor 0 ow i 0 Modern Physics Fall 2008 Dr Starovoitova Lecture 1 1 By GARY LARSON 39 quotii I SIDI A MJ i mnm 39Mrhiuwu mu Ohhhhhllh Lack al nal S lmnnr Dans an m toquot thin megaquot M comprehend quar um mac n a Review Lecture 10 Matter waves De Broglie relations Electron diffraction Waves 7x D T and k Fourier series and Fourier integral l 11 Uncertainty principle Electron in space position momentum energy time Heisenberg showed that no matter how accurate the instruments used quantum mechanics limits the precision when two properties are measured at the same time 1 AkAxZ 2 2 2 2 mp h h 1 11 Uncertainty principle 1 Man excited states are not stable gt Y AtAw 2 and decay in about AtZIO398 s Thus a AE3X10398 eV E hf h ha 27 AtAE 2 E 2 39 L 112 Heisenberg7s microscope Heisenberg pictured a microscope that obtains very high resolution by using highenergy gamma rays for illumination The microscope can resolve objects to a size of AX which is related to the wavelength 7x of the gamma ray by the expression AX I 7x 2sinA Momentum before ph 7x lMomentum after p39X h sinA 739 2Momentum after pquotX h sinA 7xquot p39X h sinA N I pquotX h sinA 7quot pquotX p39X I ApX 2h sinA 7 Since AX XZsinA and ApX 2h sinA 7x AX ApX h I 13 Implications I believe that the existence of the classical quotpathquot can he pregnantly formulated as follows The quotpathquot comes into existence only when we observe it In the sharp formulation of the law of causalityquot quotif we know the present exactly we can calculate the futurequotit is not the conclusion that is wrong but the premise Heisenberg in uncertainty principle paper 192 7 l 14 Quantum wave function 1 A wave function is a mathematical tool used in quantum mechanics to describe any physical system It is a function from a space that maps the possible states of the system into the compleX numbers The laws of quantum mechanics describe how the wave function evolves over time Quantum coral shows electron wave functions sort of 1 14 Quantum wave function 1 Ft 1 Classical Physics Quantum Mechanics Newton s 2nd Law Schrodinger Equation 13m Q Q xt Px t l 14 Quantum wave function 1 Statistical interpretation 2cix probability of finding the particle between X and X dX l Pxt L142 P P Always real and positive 1 02139 05 1 02i 05 W 02i 05 02i 05 004z392 01i 01i0025 0065 l 15 Indeterminaey Suppose you measure the position of the particle and find it at point C Question Where was it right before N The realist position at C Einstein the measurement The orthodox position wasn t really anywhere Bohr The agnostic position refuse to answer Pauli l 15 Indeterminaey The position of the particle was never undeterminate but was really unknown to the experimenter d Espagnat Observations not only disturb what has to be measured they produce it Jordan One should no more rack one s brain about the problem of whether something one cannot know anything about eXists all the same than about the ancient question of how many angels are able to sit on the point of a needle Pauli l 15 Indeterminacy Orthodox position Copenhagen interpretation Schr39ddinger s Co r A quantum particle doesn39t eXist in One state or another Radioactive but in all of its possible Material states at once It39s only When Weobserve its state that a quantum particle is essentially forced to choose 9 one probability and that39s the state that we observe Modern Physics w w w o F f t h vmuuf hcmarkxurn km o hnak by Mark Parisi39 Fall 2008 Dr Starovoitova a 39 q 0 Lecture 2 mu THE JNFNENCKQF CAVE mm Emma Review Lecture 1 Newton s laws are invariant as we shift from one coordinate system to another Classical velocityaddition formula u u V The postulates of relativity Laws of physics are invariant as we shift from one inertial frame to another In all inertial frames light travels with the same speed in all the directions c I 3 X 108 ms MichelsonMorley Experiment no motion relative to the ether frame is detected i 26 Time dilation Imagine that Bob is in a train moving to the right with some speed V relative to the gr0und on whichJackie is standing watching him go by Inside the train the ball goes up and down Outside the traln the bail appears to be going faster at has the same upanddown speed plus the forward speed of the trsln The faster the train is moving the taster the bail appears to he going to the outside observer Copyright 3239 Addison Wasiey 26 Time dilation iillii Jackie your point of View Cogyngm 2 Addison WEsfay This effect is called time dilation From your point of View time runs slower for anyone moving relative to you As the their speed approaches the speed of light time seems to stop 26 Time dilation x mirrors h I h39 t fh2x2 AM 021 D c c c J 1 1 C fl 122mg xl v2c2 26 Time dilation Gamma vs Velocity 25 2D 1 82 71v0 721 9 27 Evidence of time dilation RT Time Dilation Experiment by Hafele amp Keating 1971 H amp K transported atomic clocks around the Earth in planes they were sent firstly Eastward and then Westward To minimize the effect of the variations in the Earth s magnetic field the clocks were triple shielded Four clocks were employed and the average of their times was used to lessen the effect of changes in individual drift patterns relative to the standard clockstation at Washington D C A t 275i21 ns predicted A t 273i7 ns observed 27 Evidence of time dilation u Mesons are produced during nuclear fusion inside the sun u Mesons arrive on Earth as part of the cosmic 39wind39 u Mesons decay to form either a electron or a positron together with a neutrino and an antineutrino N NoeW 27 Evidence of time dilation Muon Decay at Best Elapsed Time gtlt10396 s N0 of Muons Surviving 0 568 373 229 145 41 62 36 ft 045 X106 5391 17 6 oo qowakwww 27 Evidence of time dilation Altitude 2000m t h ZOOOnz 099c O99gtlt300000000mS 65gtlt10 6s 6 1 N 5686 045X10 s 65gtlt106s 28 Length Contraction Spaceship Moving at the 10 the Speed of Light Spaceship Moving at the 99 the Speed of Light Spaceship Moving at the 9999 the Speed of Light 2 8 Length Contraction To derive the contraction we again consider a light clock only in this case let the clock be on its side so the motion of the light pulse is parallel to the clock39s velocity If the clock has length L0 in its rest frame the time for light to bounce from one side of the clock and back is I 11 However to an observer who sees the clock pass at velocity v the light takes more time to traverse the length of the clock when the pulse is traveling in the same direction as the clock and it takes less time for the return trip I L L 39 c v cv We know from the time dilation that I u The above three equations can be used to eliminate t and to to obtain the result L i 1 39 Y l Ml vsz Modern Physics Fall 2008 Dr Starovoitova MW 11m Nummn Lecture 16 Amway THAT Ascvmprzm 15W REALLY NECESUM w am 555 has WT 71E Powr LOW MAW1mm mm EatMW ww Review Lecture 15 Free particle x A sinkx B coskx Particle in 1D non rigid box 100 C6006 1100 A SiHUOC B COSUQC 11100 2 Ge WC Potential barrier tunneling WWW Kl WWWM L f l 6 l Classical oscillator Potential energy V kx22 Kinetic energy KE 2 m V22 Energy Iquot Kinetic f Enargy 39 II tPotential I ll Energy 39 Times H4 H2 334 l 6 l Classical oscillator F ma xAsinwtBcoswt F kx xt 00 maZ kx xAsinwt m5c kx x x EVkA22 m 5539 a2x Amplitude increases with energy Energy is not quantized 162 Quantum oscillator energy 712 82 kxz Pmtavnrtial swarm nlfrzerm M 39 2m 8x2 2 1 2 Enirm Elm I Transition H90 2 E90 39 energy 1quot WW7 N 7 Iquotquotquot I 774 712 82 lac2 1391 20 Eo n IILU 39 Emi m 2m 8x 2 quot quot l tEr ucl ar separaaim x En nha E0 2171a 2 xz raprasama the equilibrium separalion beiween the nuvlei E1 h a 162 Quantum oscillator wavefunctions hz 82 kxz E 2m 8x2 2 D D 00 2A0 x22b2 D A x x22b2 1 1 63 Diatomic molecule 60000 Vibrationa energy leveis 50009 400W 30000 Energy 1quot 20000 10600 C 0405 01 015 02 125 63 035 Interatomic dishance 1 nm 04 045 D 5 164 Timedependent Schrodinger Eq 8gp h 2H l at 0 W t 0xequot39 col 1xequot39 1 601 2 7 3 f p a 1 19 a 1xequot39 1 19 xeia 2 lt02 2xequot39 2t lto 0100b 2ltxgte ilt 2 2gt lt022 2 f r 2 f t Modern Physics Fall 2008 Dr Starovoitova MD Hmr39 5w AM new if quotM5 zg fr Mr 1 so ini r i Lecture 3 Thanks in he innovative lab Mini101161er Kranlav phvsbcs qulckw became Wantrule High39s mod papurar course Review Lecture 2 Time dilation t ytO Length contraction L LOY 3 l Galelian transformation Suppose there are two reference frames systems designated by S and S39 such that the coordinate axes are parallel S39 is moving With respect to S With velocity V in the Xdirection The clocks in both systems were synchronized at time t0 and they run at the same rate 8 S O O 3 l Galelian transformation x x39Vt x39 x Vt yy39 VZy Zzz39 Z39ZZ tf ft Inverse Galilean transformations Galilean transformations 32 Lorentz transformations S V o o x39 7x Vt x 7x39Vt39 Vy yV i2 Zf Vx39 2 7t V C f 71 39 2 c C 32 Lorentz transformations 33 Velocityaddition formula 392 ltl gt gt u u gl 39 080 070 What is the velocity of the spaceship A from the point of View of spaceship B 080 070 I 150 33 Velocityaddition formula x139 7x1 vt1 35239 7052 Vt2 My MAX VA yl39zyl yz39zyz AyVZAy Z139Z1 22222 AZVZAZ 39 vx 39 VAX tl39 7t1 v 1 t2 7t2 22 At 27At 2 c C C uxEAxVAtE 7Ax vAt2 ux v 2 7At vAxc l uxvc uy39szVAt39 Ay 2 uy 2 7At vAxc 71 uxvc uz39Az39At39 AZ 2 uz 2 7At vAxc 71 uxvc 34 Doppler effect f0 fs q Receding

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