PHYS 451: Quantum Mechanics I (Fall 2014)
Location & Contact Info
Instructor: Sergiy Bubin
Lecture Hours: TR 9:00 AM - 10:15 AM at room 8.317
Recitations: T 12:00 PM - 1:15 PM at room 7.517
Office Hours: TR 14:00-15:00 at 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 quantum-mechanical operators, wave functions, Hilbert spaces, Heisenberg uncertainty principle, Heisenberg and Schrödinger formulations of quantum mechanics and their interpretation in terms of physical observations. The course further covers the topics of potential wells, potential barriers, quantum harmonic oscillator, and the hydrogen atom. 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 at the introductory level,
some can be found in the library, and can also be very useful in this course.
Students are encouraged to explore those. Examples 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)
Homework Submission Guidelines
The submission of only answers is not acceptable. Homework must show
sufficient proof that a derivation of the solution was carried out.
Any student wishing to have the best possible grades on homework returned must:
Homework submission in paper form is strongly preferred. However, electronic submissions
via email (e.g. a pdf file of scanned pages) are acceptable for those students who are
away or must miss a class when the homework is due.
- Staple pages together and clearly indicate problem numbers
- Turn in neat and readable homework as points may be deducted otherwise
- Show work! Solutions or answers turned in without explanation will not receive full credit
Warning: Lecture materials provided below may be inclomplete
and are no substitute for notes taken in class or textbook materials
||Historical overview and timeline of quantum mechanics. Schrödinger equation and its basic properties.
||Uncertainty principle. Uncertainty principle at work in the ground state of hydrogen. Stationary states. Particle in the infinite 1D square well.
||Quantum harmonic oscillator (solution with the power series method).
Some useful plots can be viewed here.
||Commutators. Quantum harmonic oscillator (solution using lowering and raising operators).
||Probability current. Free particle in 1D.
||Review of the Dirac delta function. Delta function potential well and potential barrier.
||Finite square well.
||Formalism of quantum mechanics and its postulates.
||Dirac (bra-ket) notation.
||Schrödinger equation in 3D. Separation of variables for spherically symmetric potentials.
||The hydrogen-like atom.
||Commutation relations for the angular momentum. The ladder operator method.
||Matrix representation of the angular momentum operator.
||The rigid rotor.
||Addition of angular momenta. Clebsch-Gordan coefficients.
||Properties of Pauli matrices. Electron in magnetic field. Larmor precession of spin.
||Many-body problem in quantum mechanics. Identical particles
||Exchange interaction. Independent electron approximation for atoms. Shell structure.
||Periodic potentials. Band structure.
Found an error on this page or in any of the pdf files? Send an email to the instructor.