PHYS 451: Quantum Mechanics I - Spring 2018

Location & Contact Info
Instructor: Sergiy Bubin
Lecture Hours: Tue,Thu 10:30 AM - 11:45 AM in room 7.527
Recitations: Mon 2:00 PM - 2:50 PM in room 7.427
Office Hours: Mon 3:00 PM - 4:00 PM, Wed 12:00 PM - 1:00 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 25 hwhw01s.pdf
Homework #2 hwhw02.pdf Feb 1 hwhw02s.pdf
Homework #3 hwhw03.pdf Feb 8 hwhw03s.pdf
Homework #4 hwhw04.pdf Feb 15 hwhw04s.pdf
Homework #5 hwhw05.pdf Feb 22 hwhw05s.pdf
Homework #6 hwhw06.pdf Mar 1 hwhw06s.pdf
Homework #7 hwhw07.pdf Mar 10 hwhw07s.pdf
Homework #8 hwhw08.pdf Mar 27 hwhw08s.pdf
Homework #9 hwhw09.pdf Apr 10
Quiz Date Tasks Solutions
Quiz #1 Jan 23 quizq01.pdf quizq01s.pdf
Quiz #2 Feb 1 quizq02.pdf quizq02s.pdf
Quiz #3 Feb 8 quizq03.pdf see quizlec08.pdf
Quiz #4 Mar 29 quizq04.pdf quizq04s.pdf
Quiz #5 Apr 5 quizq05.pdf quizq05s.pdf
Quiz #6 Apr 10 quizq06.pdf quizq06s.pdf
  Exam     Date Problems Solutions
Midterm #1 Mar 10 quizmt1.pdf quizmt1s.pdf
Midterm #2 Apr 14 quizmt2.pdf quizmt2s.pdf
Final Apr 26 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 9 leclec01.pdf Introductory notes. Timeline of quantum mechanics.
Lecture #2 Jan 11 leclec02.pdf Review of basic probability theory.
Lecture #3 Jan 16 leclec03.pdf Wave-particle duality. Schrödinger equation and its key characteristics. Statistical interpretation of wave function.
Lecture #4 Jan 18 leclec04.pdf Expectation values. Momentum operator. Heisenberg uncertainty principle. Stationary states.
Lecture #5 Jan 23 leclec05.pdf Particle in infinite square well.
Lecture #6 Jan 25 leclec06.pdf Quantum harmonic oscillator.
Lecture #7 Jan 30 leclec07.pdf Fourier series and Fourier transform. Free particle.
Lecture #8 Feb 1,5 leclec08.pdf Review of Dirac delta function. Particle in delta function potential.
Lecture #9 Feb 6 leclec09.pdf Finite square well. Transmission through square rectangular barrier.
Suppl. note #01 Feb 6 lecnt01.pdf Probability Current.
Lecture #10 Feb 8 leclec10.pdf Commutators. Solution of quantum harmonic oscillator problem using creation and annihilation operators.
Lecture #11 Feb 10 leclec11.pdf Formalism of quantum mechanics.
Lecture #12 Feb 13 leclec12.pdf Dirac notation, representations, projection and identity operators, spectral decomposition.
Lecture #13 Feb 15 leclec13.pdf Cauchy-Schwarz inequality. General form of uncertainty principle. Time-evolution of expectation values. Energy-time uncertainty principle.
Lecture #14 Feb 22 leclec14.pdf Schrödinger equation in 3D. Separation of variables for spherically symmetric potentials. Spherical harmonics.
Lecture #15 Feb 27 leclec15.pdf Hydrogen-like atom.
Lecture #16 Mar 1 leclec16.pdf Reduction of two-body problem with central interaction into one-body problem. Quantum rigid rotor.
Lecture #17 Mar 13 leclec17.pdf Commutation relations for the angular momentum. The ladder operator method.
Lecture #18 Mar 15 leclec18.pdf Matrix representation of the angular momentum operator.
Lecture #19 Mar 27 leclec19.pdf Addition of angular momenta.
Lecture #20 Mar 29 leclec20.pdf Spin. Properties of Pauli matrices.
Lecture #21 Apr 3 leclec21.pdf Electron in magnetic field. Larmor precession. Stern-Gerlach experiment.
Lecture #22 Apr 5 leclec22.pdf Many-body problem in quantum mechanics. Exchange interaction.
Lecture #23 Apr 7 leclec23.pdf Shell structure of atoms.
Lecture #24 Apr 10 leclec24.pdf Chains of 1D wells. Development of bands of energy.
Lecture #25 Apr 12 leclec25.pdf Periodic potentials. Dirac comb. Band structure.

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