33-755 quantum i fall 2020 - carnegie mellon university · 2020. 8. 31. · operators a h h a 14...

33-755 QUANTUM I Fall 2020Class meets MWF 9:20 AM in Doherty Hall 2105 and remote online, and F 5:20 PM remote onlineProfessor: Mike Widom, Office 6305 Wean Hall, e-mail: widom@cmu.eduOffice Hours: Questions and discussion on Canvas/Piazza. Zoom appointments available by e-mail request.

Note related to the coronavirus: This class will meet in person for the first week of the semester, thentransition to fully remote. Zoom meeting links and recordings will be posted on Canvas. Class discussion(student questions, etc.) will take place on Piazza.

This course introduces quantum mechanics at a first-semester introductory graduate level. Prior familiaritywith basic principles and applications of quantum mechanics will be assumed at an advanced undergraduatelevel. Special attention will be paid to fundamental postulates of quantum mechanics and theirconsequences, in addition to practical applications to physical phenomena. Specific applications include:two-level systems; quantum information; harmonic oscillators, phonons and blackbody radiation; chargedparticles in magnetic fields; hydrogen atom. A course web site athttp://euler.phys.cmu.edu/widom/teaching/33-755 contains this syllabus plus links to day-by-day lecturecoverage and weekly homework assignments.

Books: The principal content of the course will be drawn from two books:1. Cohen-Tannoudji, Diu and Laloe, Quantum Mechanics, vol. 1.2. Griffiths, Consistent Quantum Theory. Available online at http://quantum.phys.cmu.edu/CQT. Also see ashort and simplified summary of the consistent histories approach.

Grading: Letter grades will be based on weekly homework assignments (20%), two midterms (20% each)and a final exam (40%). Students are welcome to collaborate on homework but the final solutions must beyour own work, written up separately. Homework assignments are listed athttp://euler.phys.cmu.edu/widom/teaching/33-755/hw.html. Your work will be handed in and grades will belisted on the course page on Canvas. Dates for midterm and final exams will be announced as they becomeavailable.

Course outline: We will cover the topics listed below in approximately the given time frames. Detailedclass coverage can be found at http://euler.phys.cmu.edu/widom/teaching/33-755/coverage/html.

Weeks 1-2. Hilbert space and physical properties. Composite systemsWeek 3. Unitary dynamics, spin 1/2 in magnetic fieldWeeks 4-5. Stochastic processes, sample spaces and interferenceWeeks 6-7. Multiple times, consistency, measurements, Quantum informationWeek 8. Wave mechanics, path integralsWeeks 9-11. Harmonic oscillator, phonons and blackbodyWeeks 12-15. Angular momentum and hydrogen atom

Hilbert Space

classicalreal axesStates are points

X pat t

Hibertspeace HJ la iz HComplex Vector space 14,7

i iiiorthogonalStates 44,14 o

closedunder scalar multiplication club CLlil addition 14 t 142 EH

Adjoint t ket IN EH bra 441 14 Tefft

Innerproduct Lull If 4419 C

all 14 full 47 1141520 norm

qq.IN7 atl2t ta 12 7 192 5 1213 t b 12 741 4 42 1 at L2 I 44147 16 12 t la T419 aIb tails 49147t

Operators A H HA 14 197 1 147 11 4

Matrix element LXI A 147 1 1 A1431 4 19

Adjoint At X1 CHAT AI x Ite.g Ext Atty KHA'The Kull Atx M 441 Ax ItLXIAt Axl

Hermitian unitaryIv tNormaloperatorsi NtN NN H HI uut utu.ITI If 14 is eigenvector of N with eigenvalueX NH 1147Then Nt X Nix 147

proof 111N 1 142112 0 541 NIH N 2 14741 N 2 Nt 147 11 Nt 23147112

2 If Nini Xil4i and N14,7 114 with Xitt then ilyproof 2jL4il4 stil NIHD KHIN 14

It Y Tickly3 It has real eigenvaluesproof H147 2142 THAT 7441 41HIX Http 1 2

4 Eigenvalues of U obey1212 1

proof 414 II 143 44 0 443 2244145 Eigenvectors span Fl Completeness