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
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.
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:
- Richard Liboff, Introductory Quantum Mechanics (4th Edition)
- Robert Scherrer, Quantum Mechanics: An Accessible Introduction
- Robert Eisberg, David O. Caldwell, and Richard J. Christman, Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles
- Ira N. Levine, Quantum Chemistry (6th Edition)
Important note: Lecture materials provided below may be inclomplete
and should not be considered a substitute for notes taken in class or textbook materials
||Introductory notes. Timeline of quantum mechanics.
||Review of basic probability theory.
||Wave-particle duality. Schrödinger equation and its key characteristics. Statistical interpretation of wave function.
||Expectation values. Momentum operator. Heisenberg uncertainty principle. Stationary states.
||Particle in infinite square well.
||Quantum harmonic oscillator.
||Fourier series and Fourier transform. Free particle.
||Review of Dirac delta function. Particle in delta function potential.
||Finite square well. Transmission through square rectangular barrier.
|Suppl. note #01
||Commutators. Solution of quantum harmonic oscillator problem using creation and annihilation operators.
||Formalism of quantum mechanics.
||Dirac notation, representations, projection and identity operators, spectral decomposition.
||Cauchy-Schwarz inequality. General form of uncertainty principle. Time-evolution of expectation values. Energy-time uncertainty principle.
||Schrödinger equation in 3D. Separation of variables for spherically symmetric potentials. Spherical harmonics.
||Reduction of two-body problem with central interaction into one-body problem. Quantum rigid rotor.
||Commutation relations for the angular momentum. The ladder operator method.
||Matrix representation of the angular momentum operator.
||Addition of angular momenta.
||Spin. Properties of Pauli matrices.
||Electron in magnetic field. Larmor precession. Stern-Gerlach experiment.
||Many-body problem in quantum mechanics. Exchange interaction.
||Shell structure of atoms.
||Chains of 1D wells. Development of bands of energy.
||Periodic potentials. Dirac comb. Band structure.
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