"Shut up and calculate!" -- N. David Mermin

**Coronavirus Impact:**Masks are required in this course. This masking policy is subject to change during the semester, and any changes will be posted clearly in Canvas announcements.**Lecturer:**Professor Randall J. Scalise**Meeting time and place:**TTh 12:30 - 1:50 pm in Clements Hall 224.**Office hours:**MWF noon-2:00pm, after lecture, and by appointment in room 107 Fondren Science Building**Contact:**- Call or leave a message at 768-2504, or
- Leave a note in the Physics Department Office - 102 Fondren Science, or
- send me e-mail: <scalise@smu.edu>

- SMU Required Syllabus Statements
**Exam Dates:**Open book, open notes, open Mathematica (or other symbolic manipulator), closed internet.- Midterm - Tuesday 5 October 2021 during the lecture meeting time via Zoom
- Final - Monday, 13 December 2021, 11:30 AM - 2:30 PM

**Mathematica tutorial:**PDF 4 pages, 32563 bytes**Grading:**- Homework - 60% (drop lowest)
- Midterm Examination - 20%
- Final Examination - 20%

**Text:**Quantum Mechanics - Volumes 1 and 2 by Claude Cohen-Tannoudji, Bernard Diu, and Frank Laloe**PHYS 5382 fall 2015 (Scalise) Lecture notes:****PHYS 6335 fall 2018 (Vega) Lecture notes:**

**Lecture Notes:**- Lecture #1 - Introduction, Placement Examination
- Lecture #2 - Mathematical Preliminaries and Notation; Zoom video
- Robert Jaffe's notes Postulates of QM
- Georgia Tech Chemistry notes - some incorrect statements about the wavefunction (it does need to be single-valued; that's correct)
- Wave function from Wikipedia
- Hilbert Space from Wikipedia
- Square-integrable function from Wikipedia
- L^p space from Wikipedia

- Lecture #3 - Mathematical Preliminaries and Notation, continued; Zoom video
- Lecture #4 - Mathematical Preliminaries and Notation, continued; Zoom video
- Poisson Bracket from Wikipedia - becomes the commutator in QM
- Measurement Problem from Wikipedia
- Sidney Coleman, Quantum Mechanics in Your Face [1994] Docoherence at 39 minutes
- How do black holes destroy information and why is that a problem? - Sabine Hossenfelder
- Hugh Everett's many-worlds interpretation from Wikipedia
- There is no quantum measurement problem
- Georg Cantor's Diagonalization Proof that the cardinality of the real numbers is larger than that of the integers

- Lecture #5 - Eigenvalues, Eigenkets, Energy Degeneracy; Zoom video
- Energy Non-Degeneracy in One Dimension from Wikipedia
- MIT course page 10, by Baron Zwiebach
- Canonical commutation relation from Wikipedia

- Lecture #6 - Review of potentials, energy eigenstates; Zoom video
- Free particle from Wikipedia
- Infinite square well (particle in a box) from Wikipedia
- Particle in two-dimensional box
- Finite square well from Wikipedia
- Finite square well bound states from MIT 8.04
- Finite square well bound states from YouTube
- Finite square well scattering states from YouTube
- Hydrogen atom from Wikipedia
- List of quantum-mechanical systems with analytical solutions from Wikipedia

- Lecture #7 - Review of potentials, energy eigenstates, continued; Zoom video
- Dirac delta potential from Wikipedia (well, barrier, double delta well)
- 2- and 3-dimensional delta potentials are different from 1-d: Llano, Nyeo, Jackiw.
- Wave functions for the triple delta well: Paul C.W. Davies Quantum Mechanics p.33
- Derivative of delta potential
- Professor John Fattaruso's 31 = Infinity Wells showing development of energy bands

- Lecture #8 - Review of potentials, energy eigenstates, continued; Zoom video
- Quantum harmonic oscillator from Wikipedia

- Lecture #9 - Review of potentials, energy eigenstates, continued; Zoom video
- Coherent States for the QHO, from Wikipedia
- Phase space {x,p} gif of a coherent state (not 2-dimensional QHO)

- Lecture #10 - Spreading of Free Particle Gaussian Wave Packet with time, Generalized Ehrenfest's Theorem; Zoom video
- Spreading of a complex wave packet in 1 dimension, visualized as a 3D coil.
- Wave Packet from Wikipedia
- Ehrenfest's Theorem from Wikipedia
- Node theorem

- Lecture #11 - Schwarz Inequality, Generalized Uncertainty Principle; Zoom video
- Cauchy-Schwarz Inequality from Wikipedia
- Uncertainty Principle from Wikipedia
- Heisenberg Picture from Wikipedia

- Lecture #12 - Robertson-Schroedinger Uncertainty Relation, Spherical Polar coordinates; Zoom video
- Laplace's equation is separable in 13 coordinate systems from Wolfram
- Associated Legendre Function of the First Kind from Wolfram
- Associated Legendre Function of the Second Kind from Wolfram

- Midterm examination - open book, open notes.

- Lecture #13 - Bound State in the Continuum, Numerical Integration; Zoom video
- On Positive Eigenvalues of One-Body Schrodinger Operators Barry Simon, Communications on Pure and Applied Mathematics, Vol. XXII, 531-538 (1967)
- When I was your age, we programmed in BASIC. And we liked it. Not really.
- First-order (forward) Euler method for solving differential equations from Wikipedia
- Runge-Kutta method from Wolfram Mathworld
- An Algebraic Approach to Reflectionless Potentials in One Dimension R.L. Jaffe
- Reflectionless Potential
- Mathematica notebook for Numerical QHO also available in PDF format

- Lecture #14 - Midterm Examination
- Lecture #15 - Hydrogen; Zoom video
- Hydrogen atom from Wikipedia
- The SO(4) Symmetry of the Hydrogen Atom by Sean J. Weinberg
- Three-Dimensional Isotropic Harmonic Oscillator and SU(3) by D. M. Fradkin
- On Accidental Degeneracy in Classical and Quantum Mechanics by Harold V. McIntosh
- Proton radius puzzle

- Lecture #16 - Hydrogen continued, Angular Momentum; Zoom video
- Fine Structure in Hydrogen from UCSD
- Fine structure from Wikipedia
- Hyperfine_structure from Wikipedia
- Hydrogen 21 cm line from Wikipedia
- Lamb shift from Wikipedia
- The Hyperfine Splitting in Hydrogen Feynman lectures
- Angular momentum operator from Wikipedia
- The Casimir Effect and the Quantum Vacuum by R.L. Jaffe

- Lecture #17 - Angular Momentum continued; Zoom video
- Lecture #18 - Angular Momentum continued; Zoom video
- Stern and Gerlach: How a Bad Cigar Helped Reorient Atomic Physics from Physics Today
- Exact hydrogen energy eigenvalues from the Dirac equation (but no finite proton size, no proton spin (hyperfine structure), and no field theory: Lamb shift, electron anomalous magnetic moment, etc.) from UC San Diego
- Hydrogen-like atom - Solution to Dirac equation from Wikipedia
- The discovery of the electron spin by S.A. Goudsmit
- Spin: The Quantum Property That Should Have Been Impossible
- Weinberg's proof of the spin-statistics theorem
- Weyl spinors and the Dirac equation

- Lecture #19 - Angular Momentum continued, Rotations, Larmor Precession; Zoom video
- Spin One audio Feynman lectures
- Spin One Feynman lectures
- Spin One-half audio Feynman lectures
- Spin One-half Feynman lectures

- Lecture #20 - Angular Momentum continued, Rotations, Pauli Matrices; Zoom video
- Pauli matrices from Wikipedia
- Lie Algebras in Particle Physics by Howard Georgi
- Lie Groups and Lie Algebras 1st of four lectures by Gang Xu (watch them all)
- Plate Trick from Wikipedia
- The Strange Numbers That Birthed Modern Algebra Quanta Magazine
- Knots and Physics, Third Edition by Louis H. Kauffman, pp427-434

- Lecture #21 - Angular Momentum continued, Rotations, Functions of a Matrix; Zoom video
- Quaternion from Wikipedia
- The Octonions by John C. Baez
- Division algebra from Wikipedia
- Tensor product from Wikipedia
- Quantum Mechanics needs complex numbers by Scott Aaronson
- Aharonov-Bohm effect from Wikipedia

- Lecture #22 - Functions of a Matrix, Helicity, Addition of Angular Momonta; Zoom video
- Lecture #23 - Addition of Angular Momonta, Clebsch-Gordan Coefficients; Zoom video
- Clebsch-Gordan Coefficients Table
- Clebsch-Gordan Coefficients from Wikipedia

- Lecture #24 - Wigner-Eckart Theorem; Zoom video
- Wigner-Eckart Theorem from Wikipedia

- Lecture #25 - Wigner-Eckart Theorem continued, Scattering; Zoom video
- Preon from Wikipedia
- Axion from Wikipedia
- The Pooltable Analogy to Axion Physics by Pierre Sikivie

- Lecture #26 - Scattering, Partial Waves; Zoom video
- Lecture #27 - Scattering, Phase Shifts, First Born Approximation; Zoom video
- Lecture #28 - EPR Paradox, Bell's Theorem; Zoom video
- EPR Paradox from Wikipedia
- John Stewart Bell's Theorem from Wikipedia
- Can Quantum Mechanical Description of Physical Reality Be Considered Complete? by A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 – Published 15 May 1935, DOI:https://doi.org/10.1103/PhysRev.47.777
- Is the Moon there when nobody looks? Reality and the quantum theory by N. David Mermin, Physics Today, April 1985, p38.
- Quantum Mysteries Revisted N. David Mermin, Am. J. Phys 58, p731, (1990)
- Sidney Coleman, Quantum Mechanics in Your Face [1994] from YouTube
- Speakable and Unspeakable in Quantum Mechanics by John S. Bell
- Quantum Computing and Entanglement - John Preskill from YouTube

- Final examination - online - Monday, 13 December 2021, 11:30 AM - 2:30 PM, open book, notes.

**Homework:**Due dates are strictly enforced. 50% if late; 0% once the solutions are posted. You may work together, but the work that you turn in should be unique. Identical work will receive a grade that is divided among all parties. It is possible to find answers to some homework problems on the internet; do not do this. The point, after all, is not to fool me into thinking that you have learned physics, but rather actually to learn some physics.- homework #1 (PDF format) - due Monday 30 August 2021 at 11:59:59pm; Read CDL chapter 3.
- homework #2 (PDF format) - due Tuesday 7 September 2021 at 11:59:59pm; Read CDL chapter 2.
- homework #3 (PDF format) - due Monday 13 September 2021 at 11:59:59pm; Read CDL chapter 1 and its complements.
- homework #4 (PDF format) - due Monday 20 September 2021 at 11:59:59pm; Read CDL chapter 5 and its complements.
- homework #5 (PDF format) - due Monday 27 September 2021 at 11:59:59pm; Read CDL chapter 2 all complements, chapter 3 complements A-C,F,K.
- No homework due on Monday 4 October 2021 because of the midterm exam on Tuesday 5 October 2021.
- No homework due on Monday 11 October 2021 because of Fall Break.
- homework #6 (PDF format) - due Monday 18 October 2021 at 11:59:59pm; Read CDL chapter 7 and its complements.
- homework #7 (PDF format) - due Tuesday 26 October 2021 at 11:59:59pm; Read CDL chapter 6 and its complements.
- homework #8 (PDF format) - due Monday 1 November 2021 at 11:59:59pm; Read CDL chapter 4 and its complements.
- homework #9 (PDF format) - due Monday 8 November 2021 at 11:59:59pm; Read CDL chapter 9 and its complements.
- homework #10 (PDF format) - due Monday 15 November 2021 at 11:59:59pm; Read CDL chapter 10 and its complements.
- homework #11 (PDF format) - due Monday 22 November 2021 at 11:59:59pm; Read CDL chapter 8 and its complements.
- No homework due on Monday 29 November because of Thanksgiving Break.
- homework #12 (PDF format) - due Monday 6 December 2021 at 11:59:59pm; Read CDL chapter 8 and its complements.

**Homework Solutions****Disability Accommodations, Religious and Excused Absences****Official University Calendar****Other Resources:**- Heisenberg and the early days of quantum mechanics by Felix Bloch
- EPR Paradox
- Is the Moon there when nobody looks? Reality and the quantum theory by N. David Mermin, Physics Today, April 1985, p38.
- Quantum Mysteries Revisted N. David Mermin, Am. J. Phys 58, p731, (1990)
- Does Bell's Inequality rule out local theories of quantum mechanics?
- Quantum 'spookiness' passes toughest test yet
- Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km

*Quantum Mechanics*by Claude Cohen-Tannoudji, Bernard Diu, and Frank Laloe*Quantum Mechanics: Classical Results, Modern Systems, and Visualized Examples*by Richard W. Robinett*Quantum Mechanics: Concepts and Applications*by Nouredine Zettili- MIT Open Courseware (Physics)
- The Theoretical Minimum - Quantum Mechanics
- Quantum Field Theory: Lecture Log
- Quantum Computing & the Entanglement - John Preskill on YouTube
- Quantum Mechanics III (Physics 125c) by Sean Carroll, Physics Department, Caltech
- Sidney Coleman, Quantum Mechanics in Your Face [1994]
- How do black holes destroy information and why is that a problem? - Sabine Hossenfelder
*Something Deeply Hidden*by Sean Carroll*Boojums All the Way Through*by N. David Mermin

"I think I can safely say that nobody understands quantum mechanics." —Richard Feynman, The Character of Physical Law (MIT Press: Cambridge, Massachusetts, 1995), 129.

"Those who are not shocked when they first come across quantum theory cannot possibly have understood it." --Niels Bohr, in a 1952 conversation with Heisenberg and Pauli in Copenhagen; quoted in Heisenberg, Werner, Physics and Beyond. (New York: Harper & Row, 1971) p. 206.

Thirty-one years ago [1948], Dick Feynman told me about his "sum over histories" version of quantum mechanics. "The electron does anything it likes,"he said. "It just goes in any direction at any speed, forward or backward in time, however it likes, and then you add up the amplitudes and it gives you the wave-function." I said to him, "You're crazy." But he wasn't. -- Freeman Dyson, 1980, in Some Strangeness in the Proportion: A Centennial Symposium to Celebrate the Achievements of Albert Einstein (Harry Woolf, editor; report of the Einstein Centennial Symposium held 4-9 March 1979 at Princeton, New Jersey) 1980, page 376 quoted in Nick Herbert, Quantum Reality: Beyond the New Physics (1985) page 53

Back to Professor Scalise's Home Page