PHYS 481: Quantum Mechanics
Spring 2025 (update in progress)
Prof. Tom Browder (WAT 233, Office Hrs: after class TuTh or by
appointment)
Grader Ammar Bayyari
Quantum Mechanics Part II
The course will meet Tu-Th 12:00-1:20 pm in WAT114, and
follow the textbook of David H McIntyre
"Quantum Mechanics, A
Paradigms Approach", Cambridge University Press (Chapters 8-14).
Recommended Reading:
David J. Griffiths, An Introduction to Quantum Mechanics, 3rd
edition, Cambridge University Press
After covering the basics,
will try to adjust the schedule to
include the EPR paradox and entangled states in the course.
- Tuesday, Jan 14; Angular momentum operators, commutation
relations (Chapter 7 & notes)
- Thursday, Jan 16; Angular momentum: raising/lowering
operators, ladder of states (Chapter 7 & Notes)
- Tuesday Jan 21; Hydrogen atom I: solve radial equation
(Chapter 8)
- Thursday Jan 23; Hydrogen atom II: radial equation solution,
continued using power series method (Chapter 8)
- Tuesday Jan 28; Hydrogen atom III: summary. Quantum numbers
and their meaning. Finding probability of a given electron
radius.
Fine structure constant. Normalization in spherical
coordinates (Chapter 8)
- Thursday Jan 30; QM Harmonic Oscillator I. Raising and
Lowering Operators. (Chapter 9)
- Tuesday Feb 4, QM Harmonic Oscillator II. Normalization of
states. Notation on Hermitian conjugation.
Raising/lowering operator for expectation
values. (Chapter 9)
- Thursday Feb 6,
Math Methods: Integrating x^2exp(-x^2).
Useful identities for raising/lowering
operators. Hermitian conjugation.
Homework hints. Even vs odd
functions. (Chapter 9)
- Tuesday Feb 11: QM Harmonic Oscillator III:
Diatomic Molecules, Ehrenfest's Theorem (Chapter 9)
Start Perturbation theory (Chapter 10)
- Thursday Feb 13:
Perturbation theory I: Non-degenerate and Degenerate Perturbation
Theory (Chapter 10)
- Tuesday Feb 18: Perturbation Theory Examples and Applications
- Thursday Feb 20: Variation Principle I,
Trial wavefunction (Griffiths Chapter 8)
- Tuesday Feb 25: Variational Principle II, Helium
(Griffiths Chapter 8)
- Thursday Feb 27, More examples: Hydrogen Ion, Hydrogen molecule
(Griffiths Chapter 8)
- Tuesday, March 4, Review for Midterm 1 (Practice problems,
review hydrogen atom and SHO)
- Thursday, March 6, Midterm 1 (3 problems: Hydrogen Atom,
SHO, Short-answer conceptual questios)
- Tuesday, March 11, Perturbation theory applied to the Hydrogen
Atom. Overview and Hyperfine structure.
Review angular momentum J.
Introduce Coupled and uncoupled bases.
- Thursday, March 13, Addition of angular
momenta. Clebsch-Gordan coefficients.
Finish Hyperfine structure
- March 17-21, Spring Break
- Tuesday March 25, Fine structure, H' = L dot S. How to
evaluate. (In-class review).
- Thursday March 27, Identical Particles in QM (fermions and
bosons)
Ground state of helium, the Periodic Table
- Tuesday April 1, Identical particles II:
Excited states of Helium, Start time-dependent perturbation theory
- Thursday April 3, Time dependent perturbation theory, part I
Fermi's Golden Rule, Electric Dipole radiation. Selection Rules.
- Tuesday April 8, Practice problems for Midterm II
- Thursday April 10, midterm II (perturbation theory (time-independent),
addition of
angular momentum, (hyper)-fine structure of hydrogen )
- Tuesday April 15, Time dependent perturbation theory, part II)
Einstein coefficients (absorption, stimulated and spontaneous
emission)
- Thursday April 17, Time dependent perturbation, part III.
- Tuesday April 22, 2S->1P transition, Adiabatic approximation,
Sudden approximation
- Thursday April 24, Adiabatic approximation example,
Bohm-Aharanov effect, WKB approximation (Griffiths)
- Tuesday April 29, WKB approximation, SHO example,
alpha decay (Griffiths)
- Thursday May 1, Scattering Theory (Born approximation)
(Griffiths)
- Tuesday May 6, Review
Final exam, Thursday May 8, 12-2 pm ,
note special time and
date
Six problems (four involve detailed calculations,
two are short-answer conceptual problems)
Major themes for the final: Time-independent perturbation theory, time-dependent perturbation
theory, addition of angular momenta, identical particles
Problems on the final may involve the SHO, hydrogen atom and a
particle in a box.
Knowledge of the fine and hyperfine
structure of hydrogen and other splittings will be
covered. A simple question on radiative transitions will be included.
Very basic knowledge of various approximations (sudden, adiabatic, WKB)
will be covered.
There will be two midterms, and a final exam.
For the two midterms and final, a calculator and a notecard are
allowed.
Grading weights:
Homework Problems (25%)
Two Midterms (30%)
In-class exercises (15\%)
Final (30%)
Midterm exam I: Thursday March 6
(Covers Chapters 8-9, bring one standard size
notecard and calculator)
Midterm exam II: Thursday April 10
(Cover Chapters 10-12, bring one standard size
notecard and calculator)
Final exam, (Covers Chap 8-14)
4 problems with detailed calculations and 2 short answer conceptual
problems
Thursday May 8, 12-2 pm ,
note special time and date
Bring crib sheet (a single page of notes is allowed) and a calculator
Substitutes Feb 20 - March 6 (Boyang Zhang, Ammar Bayyari);
Belle II upgrade meeting, Belle II General Meeting, e+e- Factory
workshop.
Last modified: April 29, 2025
(Check frequently for updates)
Tom Browder / teb#phys.hawaii.edu