Spring 2023 - PHYS 415 D100

Quantum III (3)

Class Number: 1531

Delivery Method: In Person


  • Course Times + Location:

    Mo, We, Fr 10:30 AM – 11:20 AM
    AQ 5035, Burnaby

  • Exam Times + Location:

    Apr 21, 2023
    8:30 AM – 11:30 AM
    AQ 5035, Burnaby

  • Prerequisites:

    PHYS 385; either PHYS 384 or MATH 314. All prerequisite courses require a minimum grade of C-.



Wave mechanics in three dimensions; orbital angular momentum and spherical harmonics; central potentials, hydrogen atom; time-independent perturbation theory, Stark effect, Zeeman effect; identical particles, helium atom; scattering, Born approximation; time-dependent perturbation theory, interaction picture. Quantitative.


Understand foundations of quantum mechanics. Successfully attacking theoretical problems in quantum mechanics and establishing the major physical conclusion. The topics to be covered this semester will overlap most of the material in Chaps 9-14 of Townsend’s text.

Topics to be covered in the textbook.

Ch9 Two body problem

  • Review classical and quantum mechanics
  • Symmetries: translation Ch6 and Ch9-2, time evolution Ch4, rotation Ch9-5
  • Rotational invariance Ch9-5, orbital angular momentum in position space Ch9-8, spherical harmonics, orbital angular momentum eigenfunction Ch9-9, and addition of angular momentum Ch9-9, Ch3, and Ch5
  • Two body problem: conservation of P (relative and CM coordinates) Ch9-3, conservation of J Ch9-5, commuting observables Ch9-6

Ch10 Bound states of central potential

  • Coulomb potential and Hydrogen atom Ch10-2
  • Laguerre polynomials and eigenfunctions and eigenvalues of Hydrogen atom Ch10-1 and Ch10-2
  • Energy level transition between principle quantum numbers Ch10-2

Ch11 Time independent perturbations

  • The energy levels of Hydrogen Ch11-6
  • Relativistic perturbations to the Hydrogen, L-S coupling Ch11-5, non degenerate perturbation theory Ch11-1.
  • Degenerate case Ch11-2, Stark Effect Ch11-3
  • Zeeman Effect Ch11-7
  • Paschen-Back limit Ch11-7
  • Dirac Equation – Fermions, half integer spin, positive and negative solution, particle and antiparticle (outside of the textbook).

Ch12 Identical Particles

  • Indistinguishable particles and symmetrization postulate Ch12-1 - Boson and Fermion, review of two electron system.
  • The Helium Atom Ch12-2 - excited states, para and ortho helium Ch12-2.
  • Multi-electron atoms and periodic table Ch12-3 - electronic configuration and L, S, and J Ch12-3, Covalent Bonding Ch12-4

------------------Finish Coulomb potential and back to Ch9------------------

Quantum systems beyond Hydrogen atom

  • Vibration and Rotation of a diatomic molecule Ch9-7
  • The finite spherical well and the Deuteron Ch10-3 with Ch6-9 and Ch6-10.
  • The infinite spherical well Ch10-4.
  • The 3-D Harmonic Oscillator Ch10-5.


Ch13 Scattering

  • Rutherford's experiment with alpha-particles, asymptotic wave functions and the differential cross section Ch13-1, probability density Ch6-10.
  • The Born approximation Ch13-2.
  • The Yukawa potential Ch13-3.
  • Partial wave expansion and phase shift analysis Ch13-4 and Ch13-5.



Ch14  Photons and Atoms

  • The Aharonov-Bohm effect Ch14-1.
  • Introduction of canonical momentum Ch14-2 and Ch14-4, second quantization Ch14-3.
  • Time dependent perturbation theory Ch14-5.
  • Schrodinger vs Heisenberg picture, interaction picture Ch14-5.
  • Fermi Golden Rule Ch14-6.
  • Spontaneous Emission Ch14-7.
  • Klein-Gordon equation – Bosons, more than one particle in a state with momentum P


  • Midterm 30%
  • Final Exam 40%
  • Homework 30%



Required text: John S. Townsend, A modern approach to Quantum Mechanics.

Recommended reading lists: David J. Griffiths, Introduction to Quantum Mechanics; P. A. M. Dirac, The Principles of Quantum Mechanics.


Your personalized Course Material list, including digital and physical textbooks, are available through the SFU Bookstore website by simply entering your Computing ID at: shop.sfu.ca/course-materials/my-personalized-course-materials.

Department Undergraduate Notes:

Students who cannot write their exam during the course's scheduled exam time must request accommodation from their instructor in writing, clearly stating the reason for this request, within one week of the final exam schedule being posted.

Registrar Notes:


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