EE 223 Applied Quantum Mechanics 2 Winter 2016

Transcription

1 EE 223 Applied Quantum Mechanics 2 Winter 2016 Syllabus and Textbook references Version as of 12/29/15 subject to revisions and changes All the in-class sessions, paper problem sets and assignments, and all the online lessons (e.g., 1.1) and units (e.g., 1.1.1) for this class are listed below. Mostly, there are two inclass sessions one reviewing the previous week and the other introducing new material to support the paper problems and assignments and three online lessons each week. The titles for all of these sections and the in-class lectures should give a good sense of the material being covered. Section numbers at the beginnings of the lines below (e.g., 1.2 and 1.2.3) refer to the corresponding sections (lessons or units) of the online course. The numbering here continues on from that of EE222. References below to QMSE are to sections in the book Quantum Mechanics for Scientists and Engineers by David A. B. Miller (Cambridge, 2008), which is the recommended text for this class. The due dates for the various online and paper quizzes, problem sets and assignments are also listed below. (There are no exams so no exam times are shown.) Week 10 (starting Monday 1/4/16) Monday 1/4/16 11:30 a.m. Gates B01 Session Introduction to the class (and introduction to Bravais lattices) Friday 1/8/16 11:30 a.m. Gates B01 Session Lecture/discussion Modeling a one-dimensional square periodic potential (supplementary lecture notes) Hand out supplementary lecture notes Paper Problem Set 1 handed out due 11:30 a.m. Friday 1/15/16 Posted 1/4/16. Quizzes due 12 noon, Wednesday, 1/13/16. Assignment due 12 noon Wednesday 1/13/ Quantum mechanics in crystals Introduction to quantum mechanics in crystals QMSE Chapter 8 Introduction Crystal structures QMSE Bloch theorem Periodic boundary conditions QMSE (through Eq. 8.6) Bloch theorem derivation QMSE 8.3 (from Eq. 8.7) Density of states in k-space QMSE 8.4 1

2 Week 11 (starting Monday 1/11/16) Monday 1/11/16 11:30 a.m. Gates B01 Session Review and discussion of Week 10 material. Extended discussion of emergence of band structures. Friday 1/15/16 11:30 a.m. Gates B01 Lecture k.p theory QMSE 8.9 (Note: this topic is needed for paper Problem Set 2 (handed out today) and for paper Assignment 1, which will be handed out later) Paper Problem Set 1 due 11:30 a.m. Paper Problem Set 2 handed out due 11:30 a.m. Monday 1/25/16 Posted 1/8/16. Quizzes due 11:30 a.m. Friday, 1/15/16. Assignment due 12 noon Wednesday 1/20/ Band structures Band structures QMSE 8.5 introduction Band structure diagrams QMSE Semiconductors, insulators and metals QMSE Band structures in 3D QMSE Effective mass theory Effective mass approximation QMSE 8.6 (up to ~ Eq. 8.29) Wavepackets and effective mass theory QMSE 8.6 (from ~ Eq to Effective mass approximation subsection) Semiconductor heterostructures QMSE 8.6 ( Effective mass approximation subsection) 11.3 Density of states Energy density of states in bulk crystals QMSE Quantum wells QMSE 8.8 through end of Formal separation subsection Density of states in quantum wells QMSE 8.8 from Quantum well subsection Week 12 (starting Monday 1/18/16) (Monday 1/18/16 no class (holiday)) Friday 1/22/16 11:30 a.m. Gates B01 Lecture - Emission and barriers QMSE 11.4 Paper Problem Set 3 handed out due 11:30 a.m. Friday 1/29/16 Note there are only two online lessons this week, though these are each longer than usual Posted 1/15/16. Quizzes due 11:30 a.m. Friday, 1/22/16. Assignment due 12 noon Wednesday 1/27/ Optical absorption in semiconductors Introduction to optical absorption in semiconductors 2

3 Perturbing Hamiltonian QMSE 8.10 through Form of the perturbing (with Appendix E for optional background) Direct transitions QMSE 8.10 subsection Direct valence through paragraph after Eq Transitioning from sums to integrals QMSE Total transition rate QMSE 8.10 subsection Direct valence starting above Eq through Eq Absorption coefficient QMSE 8.10 starting just above Eq Methods for one-dimensional problems Introduction to methods for one-dimensional problems QMSE Chapter 11 introduction Tunneling currents QMSE Transfer matrix method QMSE 11.2 up to Calculation of eigenenergies Transfer matrix and bound states QMSE 11.2 from Calculation of eigenenergies Penetration factor for slowly varying barriers QMSE 11.3 Week 13 (starting Monday 1/25/16) Monday 1/25/16 11:30 a.m. Gates B01 Session Review and discussion of Weeks 11 and 12 material and introduction to Assignment 1. Paper Problem Set 2 due 11:30 a.m. Assignment 1 handed out due Monday 11:30 a.m. 2/8/16 Friday 1/29/16 11:30 a.m. Gates B01 Lecture Continuation of discussion of Week 12 material and applications and use of transfer matrix and tunneling resonance programs Paper Problem Set 3 due 11:30 a.m. Paper Problem Set 4 handed out due 11:30 a.m. Friday 2/5/16 Posted 1/22/16. Quizzes due 11:30 a.m. Friday, 1/29/16. Assignment due 12 noon Wednesday 2/3/ Electron spin Introduction to electron spin QMSE Chapter 12 introduction Angular momentum and magnetic moments QMSE Spin angular momentum QMSE Operators for spin angular momentum QMSE Spin states Visualizing spin states QMSE Wavefunctions, spin and Hilbert space QMSE The Pauli equation QMSE Where does spin come from? QMSE Identical particles and exchange Scattering identical particles QMSE 13.1 up to Eq Fermions and bosons QMSE 13.1 last 4 paragraphs, and

4 States, single-particle states, and modes QMSE Exchange energy QMSE 13.4 Week 14 (starting Monday 2/1/16) Monday 2/1/16 11:30 a.m. Gates B01 Session Review and discussion of Week 13 material Friday 2/5/16 11:30 a.m. Gates B01 Lecture Planck distribution and black body radiation Paper Problem Set 4 due 11:30 a.m. Paper Problem Set 5 handed out due 11:30 a.m. Friday 2/12/16 Posted 1/29/16. Quizzes due 11:30 a.m. Friday, 2/5/16. Assignment due 12 noon Wednesday 2/10/ States of identical particles Multiple particle states QMSE Multiple particle basis functions QMSE 13.6 up to Eq Numbers of states QMSE 13.6 subsection Example numbers of states 14.2 Multiple particle distributions Thermal distributions QMSE Examples of states of multiple identical particles QMSE Quantum mechanical particles reconsidered QMSE Operators for harmonic oscillators Raising and lowering operators QMSE 15.1 up to Eq Properties of raising and lower operators QMSE 15.1 from Properties of raising Hamilton's equations QMSE 15.2 Week 15 (starting Monday 2/8/16) Monday 2/8/16 11:30 a.m. Gates B01 Session Review and discussion of Week 14 material Assignment 1 due 11:30 a.m. Friday 2/12/16 11:30 a.m. Gates B01 Lecture Review and discussion of Week 14 material (continued) Discussion of Assignment 2, and start of Review of Week 15 Paper Problem Set 5 due 11:30 a.m. Paper Problem Set 6 handed out due 11:30 a.m. Friday 2/19/16 Assignment 2 handed out due 11:30 a.m. Monday 2/29/16 Posted 2/5/16. Quizzes due 11:30 a.m. Friday, 2/12/16. Assignment due 12 noon Wednesday 2/17/ Quantizing the electromagnetic field Field modes as oscillators QMSE 15.3 subsection Description of a mode Electromagnetic mode Hamiltonian QMSE 15.3 from subsection Hamiltonian for to the paragraph after Eq

5 Quantum states of an electromagnetic mode QMSE 15.3 from two paragraphs above Eq to end of Field operators QMSE Quantum states of the electromagnetic field Number states QMSE 15.6 to end of subsection Representation of time dependence The coherent state QMSE 15.6 subsection Coherent state Sets of modes QMSE 15.7 to start of Multimode photon states Multimode photon states QMSE 15.7 subsection Multimode photon states Multimode operators QMSE 15.7 subsection Commutation relations to end 15.3 Fermion annihilation and creation operators Describing fermion states QMSE Chapter 16 introduction and Section 16.1 up to beginning of Fermion creation operators Creation operators QMSE 16.1 subsection Fermion creation operators Annihilation operators QMSE 16.1 subsection Fermion annihilation operators Mixtures of creation and annihilation operators QMSE 16.1 subsection Mixtures of creation and annihilation operators Week 16 (starting Monday 2/15/16) (Monday 2/15/16 no class (holiday)) (Wednesday 2/17/16 no class) Friday 2/19/16 11:30 a.m. Gates B01 Session Continue review of Week 15 material Paper Problem Set 6 due 11:30 a.m. Paper Problem Set 7 handed out due 11:30 a.m. Friday 2/26/16 Posted 2/12/16. Quizzes due 11:30 a.m. Friday, 2/19/16. Assignment due 12 noon Wednesday 2/24/ Fermion wavefunction and Hamiltonian operators Wavefunction operator QMSE Representing fermion Hamiltonians QMSE 16.3 up to paragraph after Eq Fermion Hamiltonians with multiple particle states QMSE 16.3 subsection Single particle fermion Hamiltonians with multiple particle states 16.2 Fermion operators and multiple particles Single-particle fermion operators QMSE 16.3 subsection Representation of general single-particle fermion operators Two-particle fermion operators QMSE 16.3 subsection Two-particle fermion operators 16.3 Interaction of different particles States with different kinds of particles QMSE Electron photon interaction QMSE

6 Rewriting perturbation theory QMSE Photon absorption QMSE 17.4 through end of subsection Absorption Week 17 (starting Monday 2/22/16) Monday 2/22/16 11:30 a.m. Gates B01 Session Continued review of Week 16 material Friday 2/26/16 11:30 a.m. Gates B01 Session Review of Week 16 and 17 absorption and emission material Paper Problem Set 7 due 11:30 a.m. Paper Problem Set 8 handed out due 11:30 a.m. Friday 3/4/16 Posted 2/19/16. Quizzes due 11:30 a.m. Friday, 2/26/16. Assignment due 12 noon Wednesday 3/2/ Spontaneous and stimulated emission Spontaneous emission QMSE 17.4 subsection Spontaneous emission Stimulated emission QMSE 17.4 subsections Stimulated emission and Multiple-photon case Total spontaneous emission rate QMSE 17.4 subsection Total spontaneous emission rate 17.2 Mixed states and the density matrix Introduction to mixed states and the density matrix QMSE Chapter 14 introduction Pure and mixed states QMSE 14.1 (first part) Mixed states with potential wells QMSE 14.1 (second part) Representing mixed states QMSE 14.2 and 14.3 up through Eq Properties of the density matrix QMSE 14.3 (remainder) Time-evolution of the density matrix QMSE The density matrix and optical absorption Induced dipole and a two-level system QMSE 14.5 through Eq Behavior of the density matrix in time QMSE 14.5 from Eq through the paragraph after Eq Behavior with oscillating field QMSE 14.5 from paragraph above Eq through Fig Density matrix and nonlinear optics QMSE 14.5 after Fig. 14.1, and 14.6 Week 18 (starting Monday 2/29/16) Monday 2/29/16 11:30 a.m. Gates B01 Session Review of Total spontaneous emission rate from Week 17. Preparation for assignment 3. Assignment 2 due 11:30 a.m. Assignment 3 handed out due 11:30 a.m. Friday 3/11/16 Friday 3/4/16 11:30 a.m. Gates B01 Lecture Review of density matrix from Week 17 Paper Problem Set 8 due 11:30 a.m. 6

7 Paper Problem Set 9 handed out due 11:30 a.m. Friday 3/11/16 Posted 2/26/16. Quizzes due 11:30 a.m. Friday, 3/4/16. Assignment due 12 noon Wednesday 3/9/ Quantum measurements and encryption Representing information QMSE Chapter 18 introduction Collapse and the no-cloning theorem QMSE 18.1 and 18.2 through No cloning theorem subsection Quantum cryptography QMSE 18.2 subsection A simple quantum encryption scheme 18.2 Quantum computing, teleportation and entanglement Entanglement QMSE Quantum computing and qubits QMSE Running a quantum computer QMSE Quantum teleportation QMSE Hidden variables and Bell s inequalities EPR paradox and hidden variables QMSE Bell s inequalities QMSE 19.1 Week 19 (starting Monday 3/7/16) Monday 3/7/16 11:30 a.m. Gates B01 Session Review of Week 18 material Friday 3/11/16 11:30 a.m. Gates B01 Session Interpretation of quantum mechanics instead of online (delayed online version release to after this lecture) Assignment 3 due 11:30 a.m. Problem set 9 due 11:30 a.m. Posted 3/11/16 after the last lecture. Note there are no quizzes or online assignments this week Interpretation of quantum mechanics The measurement problem QMSE Interpretations of quantum mechanics QMSE