PHYS 451: Quantum Mechanics - Spring 2016

Location & Contact Info
Instructor: Sergiy Bubin
Lecture Hours: Tue,Thu 12:00 PM - 1:15 PM in room 7.517
Recitations: Thu 10:30 AM - 11:45 AM in room 7.517
Office Hours: Tue 1:20 PM - 2:20 PM and Wed 3:00 PM - 4:00 PM in room 7.204 (or by appointment)
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, and some basic aspects of many-body quantum mechanics. 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 both at the introductory and more advanced level, some can be found in the library, and can also be very useful in this course. Students are encouraged to explore those. Examples of the introductory level textbooks are:
Homework Assignments
Assignment Problems Due Date Solutions
Homework #1 hwhw01.pdf Jan 21 hwhw01s.pdf
Homework #2 hwhw02.pdf Jan 28
Homework #3 hwhw03.pdf Feb 9
Homework #4 hwhw04.pdf Feb 18
Homework #5 hwhw05.pdf March 10
Homework #6 hwhw06.pdf Apr 8
Homework #7 hwhw07.pdf Apr 19
Quiz Date Tasks Solutions
Quiz #1 Jan 26 quizq01.pdf quizq01s.pdf
Quiz #2 Feb 4 quizq02.pdf quizq02s.pdf
Quiz #3 Feb 18 quizq03.pdf quizq03s.pdf
Quiz #4 Mar 3 quizq04.pdf quizq04s.pdf
Quiz #5 Apr 12 quizq05.pdf quizq05s.pdf
  Exam     Date Problems Solutions
Midterm #1 Mar 12 quizmt1.pdf quizmt1s.pdf
Midterm #2 Apr 21 quizmt2.pdf quizmt2s.pdf
Final May 4 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 12 leclec01.pdf Introductory notes. Timeline of quantum mechanics.
Lecture #2 Jan 14 leclec02.pdf Review of basic probability theory.
Lecture #3 Jan 19 leclec03.pdf Wave-particle duality. Schrodinger equation and its key characteristics. Statistical interpretation of wave function.
Lecture #4 Jan 21 leclec04.pdf Expectation values. Momentum operator. Heisenberg uncertainty principle. Stationary states.
Lecture #5 Jan 26 leclec05.pdf Particle in infinite square well.
Lecture #6 Jan 28 leclec06.pdf Quantum harmonic oscillator.
Lecture #7 Feb 2 leclec07.pdf Fourier series and Fourier transform. Free particle.
Lecture #8 Feb 4 leclec08.pdf Review of Dirac delta function. Particle in Delta-function potential.
Lecture #9 Feb 11 leclec09.pdf Finite square well. Transmission through square rectangular barrier.
Lecture #10 Feb 16 leclec10.pdf Commutators. Solution of quantum harmonic oscillator problem using creation and annihilation operators.
Lecture #11 Feb 18 leclec11.pdf Formalism of quantum mechanics.
Lecture #12 Feb 23 leclec12.pdf General form of uncertainty principle. Time-evolution of expectation values. Energy-time uncertainty principle.
Lecture #13 Feb 25 leclec13.pdf Dirac notation, representations, projection and identity operators, spectral decomposition.
Lecture #14 Mar 1 leclec14.pdf Schrödinger equation in 3D. Separation of variables for spherically symmetric potentials. Spherical harmonics.
Lecture #15 Mar 3 leclec15.pdf The hydrogen-like atom.
Lecture #15a Apr 7 leclec15a.pdf Reduction of two-body problem with central interaction into one-body problem.
Lecture #15b Apr 7 leclec15b.pdf Quantum rigid rotor.
Lecture #16 Mar 29 leclec16.pdf Commutation relations for the angular momentum. The ladder operator method.
Lecture #17 Mar 31 leclec17.pdf Matrix representation of the angular momentum operator.
Lecture #18 Apr 5 leclec18.pdf Addition of angular momenta.
Lecture #19 Apr 7 leclec19.pdf Spin. Properties of Pauli matrices.
Lecture #20 Apr 14 leclec20.pdf Electron in magnetic field. Larmor precession. Stern-Gerlach experiment.
Lecture #21 Apr 19 leclec21.pdf Many-body problem in quantum mechanics. Exchange intteractions.
Lecture #22 Apr 26 leclec22.pdf Shell structure of atoms.
Lecture #23 Apr 28 leclec23.pdf Periodic potentials. Band structure.

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