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P423 Quantum Mechanics II

Instructor:
Office: Elliott 118
Office hours: Mondays 2:30-3:30pm
Email: aritz@uvic.ca
Lectures: 11:30-1:00pm, Mon & Thurs 
Prerequisites: PHYS 321A, 323, MATH 301, 342, 346

This is a 4th year course on topics in quantum mechanics, and covering the following broad areas:
  • Atoms and electromagnetism
  • Scattering
  • Path integrals
  • Quantum information
  • Relativistic QM and QFT

See the course syllabus for further details.

Territory Acknowledgement: We acknowledge and respect the Lək̓ʷəŋən (Songhees and Esquimalt) Peoples on whose territory the university stands, and the Lək̓ʷəŋən and W̱SÁNEĆ Peoples whose historical relationships with the land continue to this day.


This is a 4th year course on quantum mechanics, and (time permitting) will cover the following topics. 
  • Overview
    • Introduction, review of the hydrogen atom
     
  • Atoms and electromagnetism
    • Perturbation theory
    • Fine structure
    • Atoms and electromagnetic interactions
     
  • Scattering
    • Scattering in 1D and resonances
    • Scattering in 3D
    • Lattices and band gaps
     
  • Path integrals
    • Transition amplitudes
    • Instantons and tunneling
  • Quantum information
    • Entanglement
    • Density matrices
  • Relativistic QM and QFT
    • Causality
    • Intro to QFT

The course will include a comprehensive set of lecture notes, and will not follow one specific textbook. However, there are many good texts that cover material relevant for this course. The book currently used for PHYS 323 is a good example, and will be a useful reference:

  • Quantum Mechanics, D.H. McIntyre (parts of Ch. 4, 6, 10 - 16)

There are a number of other good textbooks that cover similar material, although the approach varies, with some following a wave mechanics formalism, while others empashize the operator approach:

  • An Introducton to Quantum Mechanics, D.J. Griffiths & D.F. Schroeter
  • A Modern Approach to Quantum Mechanics, J.S. Townsend
  • Modern Quantum Mechanics, J.J. Sakurai & J. Napolitano

There are also classic texts, that can be useful as references, and with content and varied applications that extend beyond the scope of this course:

  • Quantum Mechanics, L.D. Landau & E.M. Lifschitz
  • The Principles of Quantum Mechanics, P.A.M. Dirac
 

Further online material for the course, including:

  • course notes
  • assignment sheets
  • sample solutions
will be available at the PHYS 423 course page in

The course will be assessed according to the following three components:

  • Assignments: 35%
  • Mid-term quiz: 25%
  • Final exam: 40%

There will be 5 assignments during the semester, and you will generally have ~1.5 weeks to complete each of them. The cumulative assignment grade will be computed from the top 4, with the lowest grade discarded. Assignments form an integral part of the course, used to expand on the material in the lectures in various ways. Investing time in them is beneficial for understanding the novel concepts involved in the theory of general relativity, and a key to success in this course.

Dates for the mid-term quiz and final exam are TBA.

The final grade will follow the University's percentage grading scheme, with the following universal conversion between letter and percentage grades:

  • A+  (90-100)
  • A    (85-89)
  • A-   (80-84)
  • B+  (77-79)
  • B    (73-76)
  • B-   (70-72)
  • C+  (65-69)
  • C    (60-64)
  • D    (50-59)
  • E    (TBD)
  • F    (0-49)

If the application of this scheme would result in grades deemed by the instructor to be inconsistent with the University's grading descriptions, percentages will be assigned which are consistent with them.

Note on the use of calculators in exams: Calculators are not really required for this course, but a reminder about the general university policy; "On all examinations the only acceptable calculator is the Sharp EL-510R. This calculator can be bought in the Bookstore for about $10. DO NOT bring any other calculator to the examinations."

After completing the course, you will:

  • have detailed knowledge of how quantum mechanics explains features of atomic structure.
  • be able to apply perturbative techniques to determine corrections to energy levels in hydrogenic systems.
  • have detailed knowledge of how atomic systems interact with electrostatic and magnetostatic fields.
  • have an understanding of quantum mechanical scattering and the properties of the scattering matrix. 
  • have acquired a basic understanding of the path integral formalism of quantum mechanics
  • have acquired basic knowledge of quantum entanglement, density matrices, and quantum information.
  • have acquired a basic understanding of relativistic quantum mechanics, and how the formalism of quantum field theory leads to particle states.
  • be able to communicate basic principles and complex topics in quantum mechanics in a clear and pedagogical way.