Physics 501- Spring 2022
Quantum Mechanics II
Note: Lectures will begin Monday Jan10 2022. 12:30 on Zoom.
email email@example.com for zoom logon particulars.
Midterm test 1:00 hr Mon Feb 28 Rm 302 Henn 12:30
Note: I send emails to the class via the registrar's email lists for
this course. Please make sure that you have registered your email with the
Unfortunately some service providers see this as an indication that this
is spam and dumps the mail into a junk, or spam, or other labeled
folder. I do not know how to get around this as I do not want to give
everyone everyone else's email, I do not want to enter all 50 separate
email addresses as separate emails, but I want people to get them.
Please remember to look into your junk/spam/... folder as well if you do not
get the emails for this class.
Plagerism, cheating, etc
In one word
Ian Cavers (Associate Dean of Science) has already sent more cheating cases from Science to the President's Advisory
Committees on Student Discipline (PACSD) than PACSD normally deals with in a full year from the
whole university, and he is doing a lot of filtering. So please -
- Talk to your students early in course about cheating - what it is, why they should not do
it, and even though it is easier to do it now, it is easier to catch as all the necessary
evidence is readily available.
- Be explicit and detailed about integrity expectations in your posted course outline and exam
- Tell students what happens if they are suspected of cheating:
- Interview with instructors and undergraduate chair, and if response is unsatisfactory -
- Zero on course component (e.g. exam) and report sent to Dean's Office, then -
- Interview with the Associate Dean, then -
- At least: Letter of reprimand on permanent file
- More serious cases and all second offences: Move to President's Disciplinary
Committee, with consequences up to and including expulsion
There is apparently a UBC graduate Student chat channel where you can drop in to talk with
other grad students.
https://discord.com/invite/5ANvWbfFeB I have no idea how this works, but it may offer a place where you can meet up with other students taking this course to discuss problem, assignments, confusions, etc. I have no used it so cannot offer any advice. If anyone wants to give more information, pls email me, and I can post it here.
The existence and structure of the final exam is still open for decision/discussion.
I will let you know via email what the decision is.
At present the following are the topics covered in last year's course. I may well change the order or topics
- Review of Quantum Mechanics
- Complementarity,Entanglement,Delayed Choice,
- Bell's Thm, Hardy's System, and the difference between quantum
theory and Classical theory.
- Conditions in QM (Aharonov's study of setting conditions at past
and future times)
- Linear Quantum Field theory (Bosonic theories, Simple Harmonic
Oscillator, squeezed states)
Previous Year Topics These may well get promoted to current.
- Particles and Detectors
- Hawking Radiation and Bugoliubov
- Application to quantum noise in Ligo
- Introduction to Quantum Computing (Grover, Shor, and Quantum bit
These are notes from last year supplemented by notes from this year.
- Heisenberg Schroedinger
representations, an expmaple of going from
Heisenberg to Schroedinger, Unitary evolution and
Magnus expansion. Corrections Jan 11 2021
- Unitary transformation,
Interaction representation, Example of use of
- Entanglement, density matrix
and measurement model
- Density Matrix
- Complementarity, delayed
choice, quantum eraser (Ch 8 from Zubairy's new
book "Quantum Mechanics for beginners")
- Bell's Thm, Hardy's system, and
- Heisenberg from 1930-- The Physical Principles of Quantum
The uncertainty principle refers to the degree of indeterminateness in the possible present
knowledge of the simultaneous values of various quantities with which the quantum theory deals; it does not
restrict, for example, the exactness of a position measurement alone or a velocity measurement alone. Thus
suppose that the velocity of a free electron is precisely known, while the position is completely unknown.
Then the principle states that every subsequent observation of the position will alter the momentum by an
unknown and undeterminable amount such that after carrying out the experiment our knowledge of the electronic
motion is restricted by the uncertainty relation. This may be expressed in concise and general terms by saying
that every experiment destroys some of the knowledge of the system which was obtained by previous
This formulation makes it clear that the uncertainty relation does not refer to the past: if the
velocity of the electron is at first known and the position then exactly measured the position for times
previous to the measurement may be calculated. Thus for the past times �~Tx�~Tp is smaller than the usual limiting
value, but this knowledge of the past is of a purely speculative character, since it can never (because of
the unknown change in momentum caused by the position measurement) be used as an initial condition in any
calculation of the future progress of the electron and thus cannot be subjected to experimental verification.
It is a matter of personal belief whether such a calculation concerning the past history of the electron can
be ascribed any physical reality or not.
- Einstein, Richard Tolman, and Boris Podolsky, Knowledge of Past
and Future in Quantum Mechanics. Phys Rev D 37 780-781 (1931)
- Two time conditions for a two
- Aharonov Bergman and
Lebowitz Time symmetric quantum mechanics.
- Weak Measurements and Weak Values.
- A series of
movies showing what the effect is of
decreasing the accuracy of the measurements for a
two-time spin 12.5 system.
- How to measure the spin
of a spin 1/2 particle and obtain a spin of 100
- Mean King Problem How to know what the value of sigma-x, sigma-y or sigma-z is of a two level system. "A procedure is described whereby the result of the measurement of any of the three Cartesian components of the spin of a single spin- —, particle at a single time can be inferred with certainty from the result of two other measurements, one of which is carried out before, and the other after, the time in question"
- Vaidman Bomb detector -- Or
- Book-ch 4 This is
a chapter from a book being written by R Schuetzhold and me.
- Norm for modes and associated Annihilation
- Norm and Frequency It is the norm of
a mode, not its temporal frequency which determines which is
associated with the Annihilation operators.
- "Assymptotic Adiabatic approximation for time
dependent Harmonic Osciallator"
- A Simplified Landau Zenner derivation
- Particle creation by expanding Universe
- Interaction Representation and
- Accelerated Detector The calculation
that an accelerated detector in the Minkowski vacuum state is
excited at a thermal rate.
- Negative Frequencies, Cherenkov
emission and squeezing
- Dispersion relation for
superfluid liquid He When the velocity through the
fluid becomes great enough to there is a region of wavenumber
where the frequency becomes negative on a branch where the
norm is positive. This allow quantum creation between modes
with negitive frequency and positive norm (Annihilation
operators) and the same negative frequency and negative norm
(creation operators) giving mode mixing and pair creation. The
difference in momentum is absorbed by the particle which
implies a force on the particle.
- Unruh-Wald-- detection of a
particle by accelerated detector and causality
- Notes for recent talk to IQSE,
Texas A&M on radiation and detector emission
(small modifications Apr 8 2022)
- Recent paper on the
detection by two detectors and paradoxical results thereof
- Amplifier model (interaction constants
altered to agree with that used in lecture.-Mar 23)
- "popular talk on Gravitational
radiation and the quantum Ligo detector"
- One of the very
early papers (1979) on the quantum nature of gravitational wave
detectors, including laser detectors.
- Laser Interferometer detection
of force on a Mirror
- Handwritten notes on the effect of laser
beam on radiation pressure quantum fluctuations on
- Caves 1980 PRL showing that
radiation pressure fluctuations add noise to interferometer.
- Original paper on laser noise
- Noise in Interferometer Hand
- Notes on Quantum Interferometer
II (some of this replaces the previos notes, and
- Hung Ou Mandel
- Beamsplitter calc and Hung
Ou Mandel effect
- quantum computing intro and
- First paper on Adiabatic Quantum
Computing by Farhi et al.
- Varieties of Q Compting Hand
written notes ( for an amplification of the Adiabatic thm
derivation see HERE
(altered Apr2-18:30 to include Berry's phase)
- Error Correction (Includes
diagramatic representation of Quantum Gates)
Error correction notes
- Quantum Fourier Transform and
- Diagram of Fourier Transform
- Diagram of Shor Algorithm
Assignments and Solutions
The assignements and solutions are included in pdf form.They can be viewed
with Acroread Acrobat Reader (Acroread) or if you run Linux, with gvi,okular,
If not handed in in class, put assignments into box on shelf outside my
room (in 311 Hennings) labeled Phys 341. (Not into the metal sorting rack but into the box)
The box is inside Rm 311 Hennings-- go right into the room up to the table,
then turn right. The shelf is on your right. My office is straight ahead of