PHYS 451: Quantum Mechanics I - Spring 2017

Location & Contact Info
Instructor: Sergiy Bubin
Lecture Hours: Tue,Thu 12:00 PM - 1:15 PM in room 7.427
Recitations: Fri 1:00 PM - 1:50 PM in room 7.427
Office Hours: Tue,Thu 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 19 hwhw01s.pdf
Homework #2 hwhw02.pdf Jan 31 hwhw02s.pdf
Homework #3 hwhw03.pdf Feb 7 hwhw03s.pdf
Homework #4 hwhw04.pdf Feb 14 hwhw04s.pdf
Homework #5 hwhw05.pdf Feb 23 hwhw05s.pdf
Homework #6 hwhw06.pdf Mar 2
Homework #7 hwhw07.pdf Mar 9
Homework #8 hwhw08.pdf Mar 28
Homework #9 hwhw09.pdf Apr 13
Quiz Date Tasks Solutions
Quiz #1 Jan 24 quizq01.pdf quizq01s.pdf
Quiz #2 Feb 2 quizq02.pdf quizq02s.pdf
Quiz #3 Feb 10 quizq03.pdf quizq03s.pdf
Quiz #4 Feb 21 quizq04.pdf quizq04s.pdf
Quiz #5 Feb 23 quizq05.pdf quizq05s.pdf
Quiz #6 Apr 7 quizq06.pdf quizq06s.pdf
Quiz #7 Apr 11 quizq07.pdf quizq07s.pdf
  Exam     Date Problems Solutions
Midterm #1 Mar 17 quizmt1.pdf quizmt1s.pdf
Midterm #2 Apr 14 quizmt2.pdf quizmt2s.pdf
Final Apr 29 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 10 leclec01.pdf Introductory notes. Timeline of quantum mechanics.
Lecture #2 Jan 12 leclec02.pdf Review of basic probability theory.
Lecture #3 Jan 17 leclec03.pdf Wave-particle duality. Schrodinger equation and its key characteristics. Statistical interpretation of wave function.
Lecture #4 Jan 19 leclec04.pdf Expectation values. Momentum operator. Heisenberg uncertainty principle. Stationary states.
Lecture #5 Jan 24 leclec05.pdf Particle in infinite square well.
Lecture #6 Jan 26 leclec06.pdf Quantum harmonic oscillator.
Lecture #7 Jan 31 leclec07.pdf Fourier series and Fourier transform. Free particle.
Lecture #8 Feb 2 leclec08.pdf Review of Dirac delta function. Particle in delta function potential.
Lecture #9 Feb 7 leclec09.pdf Finite square well. Transmission through square rectangular barrier.
Lecture #10 Feb 9 leclec10.pdf Commutators. Solution of quantum harmonic oscillator problem using creation and annihilation operators.
Lecture #11 Feb 14 leclec11.pdf Formalism of quantum mechanics.
Lecture #12 Feb 16 leclec12.pdf Cauchy-Schwarz inequality. General form of uncertainty principle. Time-evolution of expectation values. Energy-time uncertainty principle.
Lecture #13 Feb 21 leclec13.pdf Dirac notation, representations, projection and identity operators, spectral decomposition.
Lecture #14 Feb 23 leclec14.pdf Schrödinger equation in 3D. Separation of variables for spherically symmetric potentials. Spherical harmonics.
Lecture #15 Feb 28 leclec15.pdf The hydrogen-like atom.
Lecture #16 Mar 2 leclec16.pdf Reduction of two-body problem with central interaction into one-body problem. Quantum rigid rotor.
Lecture #17 Mar 7 leclec17.pdf Commutation relations for the angular momentum. The ladder operator method.
Lecture #18 Mar 9 leclec18.pdf Matrix representation of the angular momentum operator.
Lecture #19 Mar 28 leclec19.pdf Addition of angular momenta.
Lecture #20 Mar 30 leclec20.pdf Spin. Properties of Pauli matrices.
Lecture #21 Apr 4 leclec21.pdf Electron in magnetic field. Larmor precession. Stern-Gerlach experiment.
Lecture #22 Apr 6 leclec22.pdf Many-body problem in quantum mechanics. Exchange interaction.
Lecture #23 Apr 11 leclec23.pdf Shell structure of atoms.
Lecture #24 Apr 13 leclec24.pdf Periodic potentials. Band structure.
Lecture #25 Apr 18 leclec25.pdf Density matrix.
Lecture #26 Apr 20 leclec26.pdf Time evolution operator. Schrodinger, Heisenberg, and interaction pictures.

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