PHYS 451: Quantum Mechanics I - Spring 2020

Location & Contact Info
Instructor: Sergiy Bubin
Lecture Hours: Tue,Thu 10:30 am - 11:45 am in room 7.427
Recitations: Tue 12:00 pm - 1:15 pm in room 7.427
Office Hours: Tue 4:00 pm - 5:00 pm, Thu 12:00 pm - 1:15 pm in room 7E.333 (or by appointment)
Office Phone: +7 (7172) 69 46 63
Course Description
In this course, students learn the basics of non-relativistic quantum mechanics. The course introduces the concept of the wave function, its interpretation, and covers the topics of potential wells, potential barriers, quantum harmonic oscillator, and the hydrogen atom. Next, a more formal approach to quantum mechanics is taken by introducing the postulates of quantum mechanics, quantum operators, Hilbert spaces, Heisenberg uncertainty principle, and time evolution. The course ends with topics covering the addition of angular momenta, spin, emergence of energy bands in periodic systems, and some basic aspects of many-body quantum mechanics, such as the indistinguishability of identical particles and electron orbitals in atoms. The course will include two lectures per week accompanied by a recitation.
Course Info
Syllabus: syllabussyllabus.pdf
Required Textbook
David J. Griffiths, Introduction to Quantum Mechanics (2nd Edition)
Other Useful References
Many other texts exist on quantum mechanics, including those at the introductory level. Some can be found in the library, and may also be very useful in this course. Students are encouraged to explore those. Examples are:
Homework Assignments
Assignment Problems Due Date Solutions
Homework #1 hwhw01.pdf Jan 28 hwhw01s.pdf
Homework #2 hwhw02.pdf Feb 6
Homework #3 hwhw03.pdf Feb 13
Homework #4 hwhw04.pdf Feb 20
Homework #5 hwhw05.pdf Feb 28
Online Homework #6 hwhw06.pdf Apr 14 hwhw06s.pdf
Online Homework #7 hwhw07.pdf Apr 20 hwhw07s.pdf
Online Homework #8 hwhw08.pdf Apr 27 hwhw08s.pdf
Quiz Date Tasks Solutions
Quiz #1 Feb 4 quizq01.pdf quizq01s.pdf
Quiz #2 Feb 11 quizq02.pdf see pages 5-6 in quizlec08.pdf
Quiz #3 Feb 25 quizq03.pdf quizq03s.pdf
Online Quiz #4 Apr 9 quizq04.pdf quizq04s.pdf
Online Quiz #5 Apr 21 quizq05.pdf quizq05s.pdf
Quiz #6 Apr 23 quizq06.pdf quizq06s.pdf
  Exam     Date Problems Solutions
Midterm #1 Mar 10 quizmt1.pdf quizmt1s.pdf
Midterm #2 Apr 16 quizmt2.pdf quizmt2s.pdf
Final Apr 30 quizfin.pdf quizfins.pdf
Lecture Materials
Important note: Lecture materials provided below may be inclomplete and should not be considered a substitute for notes taken in class or textbook materials
  Lecture        Date   File Topic
Lecture #1 Jan 14 leclec01.pdf Introductory notes. Timeline of quantum mechanics.
Lecture #2 Jan 16 leclec02.pdf Review of basic probability theory.
Lecture #3 Jan 21 leclec03.pdf Wave-particle duality. Schrödinger equation and its key characteristics. Statistical interpretation of wave function.
Lecture #4 Jan 23 leclec04.pdf Expectation values. Momentum operator. Heisenberg uncertainty principle. Stationary states.
Lecture #5 Jan 25 leclec05.pdf Particle in infinite square well.
Lecture #6 Jan 30 leclec06.pdf Quantum harmonic oscillator.
Lecture #7 Feb 4 leclec07.pdf Fourier series and Fourier transform. Free particle.
Lecture #8 Feb 6,11 leclec08.pdf Review of Dirac delta function. Particle in delta function potential.
Lecture #9 Feb 11 leclec09.pdf Probability current.
Lecture #9 Feb 13 leclec10.pdf Finite square well. Transmission through square rectangular barrier.
Lecture #11 Feb 18 leclec11.pdf Commutators. Solution of quantum harmonic oscillator problem using creation and annihilation operators.
Lecture #12 Feb 20 leclec12.pdf Formalism of quantum mechanics.
Lecture #13 Feb 25 leclec13.pdf Dirac notation, representations, projection and identity operators, spectral decomposition.
Lecture #14 Feb 27 leclec14.pdf Cauchy-Schwarz inequality. General form of uncertainty principle. Time-evolution of expectation values. Energy-time uncertainty principle.
Lecture #15 Mar 10 leclec15.pdf Schrödinger equation in 3D. Separation of variables for spherically symmetric potentials. Spherical harmonics.
Lecture #16 Mar 12 leclec16.pdf Hydrogen-like atom.
R. assgn. #17 Mar 30 leclec17.pdf Reduction of two-body problem with central interaction into one-body problem. Quantum rigid rotor.
Lecture #18 Apr 7 leclec18.pdf Commutation relations for angular momentum. Ladder operator method for angular momentum.
Lecture #19 Apr 7 leclec19.pdf Matrix representation of angular momentum operator.
Lecture #20 Apr 9 leclec20.pdf Addition of angular momenta.
Lecture #21 Apr 14 leclec21.pdf Spin. Properties of Pauli matrices.
Lecture #22 Apr 14 leclec22.pdf Electron in magnetic field. Larmor precession. Stern-Gerlach experiment.
Lecture #23 Apr 16 leclec23.pdf Many-body problem in quantum mechanics.
Lecture #24 Apr 21 leclec24.pdf Exchange interaction.
Lecture #25 Apr 21 leclec25.pdf Atoms. Shell structure. Atomic terms. Hund's rules.
Lecture #26 Apr 23 leclec26.pdf Chains of 1D wells. Development of bands of energy.
R. assgn. #27 Apr 23 leclec27.pdf Periodic potentials. Dirac comb. Band structure.

Schedule of Zoom Meetings (participation requires password)
  Meeting   Date/Time Link
Meeting #18 Apr 7, 10:30am
Meeting #19 Apr 7, 12:00pm
Meeting #20 Apr 9, 10:30am
Meeting #21 Apr 14, 10:30am
Meeting #22 Apr 14, 12:00pm
Meeting #23 Apr 16, 10:30am
Meeting #24 Apr 21, 10:30am
Meeting #25 Apr 21, 12:00pm
Meeting #26 Apr 23, 10:30am

Video Recordings (authorized users)
Video recordings of Zoom meetings are available in this lecfolder on a shared Google Drive
Online Assignment Submission (authorized users)
All online assignments (homeworks, quizzes, exams) should be submitted via Google Classroom

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