c z c z c z c z c c c c a a c A P( a ) a c a z c x z R j z z, z z z z I

Transcription

1 . Quatu Spi States State Vectors c c i Ier Products: * * c c oralied. orthogoal c c c c c c * * i ii Probability that a particle i state ca be foud i state. c. States i S -basis y i i Geeral States. c a. ii Epectatio value: i y i c * a * i i c c a a c A P( a ) a c a iv. Ucertaity: A ( A A ) A A d. Matri Represetatios i S -basis c c c c i c * * * * c c c. Operators Rotatios i R( d k ) J d J / i ( ) ij R k e ii R( ) Proectios (Spi ½) ( ) R P P I

2 i P P P P P P c. Matri Represetatios of Operators A i A d. Coutators [ J J ] i J [ J J ] i J [ J J ] i J y y i y i Coutig operators have siultaeous eigestates. 3. Matri/Operator Types A A t Adoit * 4. Operator Relatios J J J J y J J ij y Uitary A A I Heritia c. J J J J J J J J J J 5. Eigevalues ad Eigestates J ( ) J 6. Raisig ad Lowerig Operators J ( ) ( ) 7. Matri Represetatios (Note siilarity betwee J s ad S s) A A A A A P c. e Rk 8. Chage of Basis i / P e i / A A ' R ' S Basis ' S Basis R A A A A A A S basis c. where S A A S AS d. Spi ½ - S σ i ters of Pauli spi atrices.

3 i S Sy S i A ' A where is the row ' is the colu ad e. Matri Eleets: ' oe proceeds i the order. f. 3D Rotatio atrices g. cos si cos si ( ) cos si S S( ) S i ( k) si cos si cos si cos h. Spi i S S i i S y i S S S Spi- Represetatio: A A A A A A A A A A C 9. Ucertaity AB for [ A B] ic ad A B C Heritia. Sed particles with spi s through Ster-Gerlach device orieted i differet positios. Deterie the uber of bea chaels ad the probability a give particle will be foud i a give chael.. Tie Evolutio: / ( ) iht t U( t) () e () d i ( t) H ( t) ( t) dt Schrödiger Equatio c. d ( ) i [ A t H A] A ( t) dt t. Hailtoias: A H B S H S S ge 3. Precessio of Spi: S S cos t Sy sit B c

4 4. Additio of Agular Moeta Eigestates of Total Agular Moeta two particles i i i R d d d S d S S S S S S S S S S S S S S S c. 5. Cotiuous States da a a a' a ( a' a) p p p p. c. / T( a) e ipa T( a) a d. p e. i ip/ p d p e d 6. Schrödiger s Equatio H ( ) V i t D Tie Idepedet: d V ( ) E d V ( ) E c. 3D Tie Idepedet: 7. Eergy eigestates: H E E E E 8. Oe Diesioal Probles Ehrefest s Theore E Free particle defiitio ad tie evolutio d p d p dv d dv dt dt d dt d ip/ c. Gaussia wave packet - e d - Coputig Gaussia itegrals p p p ad ucertaity p d. Particle i Bo Ifiite Square Well ( ) si E a a a e. Fiite Square Well f. Boud states ad scatterig states g. Reflectio Trasissio probabilities e d

5 h. Tuelig Haroic Oscillator i H a a [ a a ] a a ii a a p i a a iv. v. d E d E 4 / v a e! 9. Two-body Proble H E E E ( ) L E E c. L E E d. [ L L ] i L etc. y e. L si cot cos L L y cos cot si i i i f. Raisig ad lowerig operators: i L e i cot - applied to i i ce si L ( ) ( ). Here ( ) ( )! c.! 4 i g. Spherical Haroics Y ( ) P (cos ) e h. Hydroge Ato ( ) Zke E r r i ( r ) R( r) Y ( ) ii k e c E Z Z Z 4 3.6eV

6 iv. a o ke.59 A c c Deutero Model R( r) ru( r) '' u V u Eu r a k ta ka q. Ifiite Square Well spherical Bessel fuctios ad Magic Nubers. Tie Idepedet Perturbatio Theory H H H () () () H E Eergy Shift: E c. Wave fuctio: H () () () H () () () () k () () k E Ek d. Degeerate States ( H ) i H i () () () ( H ) ( H ) c c E ( H) ( H) c c e. Stark Effect H μ e E er f. Spi-orbit Couplig Zke H μ B SL 3 c r g. Darwi Ter Relativistic Correctio h. Fie ad hyperfie structure fie structure costat Zeea Effect e e H μ B L SB c c. Perturbatios of: particle i a bo (D D 3D) haroic oscillators (D D 3D) Spi systes (Spi ½ Spi etc.)