The
text above and at the update point is the current timeline of the
course. The text below the update point is from the same course that I
taught in fall 2014. The update point will be moving down and the
timeline will be progressively updated according to the current semester. The
date for the final exam is exact, but a date for the midterm exam will be
determined later.
|
Week
1 |
|
|
Monday,
August 31 |
·
History
of quantum mechanics - Raleigh-Jean's paradox, Planck's radiation law, Photo
electric effect (photons) ·
Wave-particle
duality, superposition principle (Sec. 1.2 - SCH) |
|
Wednesday,
September 3 |
·
Photon
interferometers, (Sec. 2.1 - SCH) ·
complex
amplitudes, beam splitters (Sec. 2.1 - SCH) |
|
Friday,
September 5 |
·
matrix
methods, testing bombs (Sec. 2.1 - SCH) ·
Particles
with spin-1/2, Stern Gerlach |
|
Week
2 |
|
|
Monday,
September 8 |
·
Labor day |
|
Wednesday,
September 10 |
·
bras-kets,
measurements and filters (Sec. 2.2-SCH) |
|
Friday,
September 12 |
·
[Intro.
To operators]Preliminary energy spectrum and time evolution, spins (Sec.
2.3-SCH) ·
Hilbert
space and postulates of QM (Sec. 3.1-SCH) ·
Operators
and matrices (Sec. 3.2 - SCH) |
|
Week
3 |
|
|
Monday,
September 15 |
·
Observables
and Expectations (Sec. 3.3-SCH) ·
Adjoints - hermitean, positive, anti-hermitean, unitary, normal operators (Sec. 3.4- SCH) |
|
Wednesday,
September 17 |
·
Eigenvalues
and Eigenvectors. (Sec. 3.5 - SCH) |
|
Friday,
September 19 |
·
Degeneracy
and commuting observables (Sec. 3.5-SCH) |
|
Week
4 |
|
|
Monday,
September 21 |
·
Continuous
Hilbert space, position, translations and momenta (Sec 1.6, SAK) |
|
Wednesday,
September 23 |
·
Commutation
relations(Sec. 1.6 SAK) |
|
Friday,
September 25 |
·
Finite
translations, position rep of momentum (1.6 SAK) ·
Wave-functions
in position space (Sec. 1.7 SAK) ·
Wave-functions
in momentum space (Sec. 1.7 SAK) ·
Wave
-packets (Sec. 1.7 SAK) |
|
Week
5 |
|
|
Monday,
September 29 |
·
Heisenberg
Uncertainty relation (Sec. 4.5 - SCH) ·
Quantum
cryptography (Sec. 4.4 - SCH) |
|
Wednesday,
October 1 |
·
Composite
systems (Sec. 6.1 - SCH) ·
Interaction
and Entanglement (Sec. 6.2-SCH) |
|
Friday,
October 3 |
·
EPR
paradox - local hidden variables (Sec. 6.5 - SCH) ·
GHZ
states version of Bell’s inequality (Sec. 6.7 - SCH) |
|
Week
6 |
|
|
Monday,
October 5 |
·
Quantum
versus classical uncertainty, density operators (Sec. 8.1 - SCH) ·
Bloch
sphere (Sec. 8.4- SCH) ·
Canonical
ensembles and von Neumann entropy (Sec. 8.6,8.6-SCH) ·
Entanglement
entropy |
|
Wednesday,
October 7 |
·
The
Schrodinger equation for the time evolution operator (Sec 2.1 -SAK) ·
Energy
Eigenkets, time dependence of expectation values |
|
Friday,
October 9 |
·
Spin
Precession ( Sec. 2.1 - SAK) ·
Time
evolution of density matrices, Bloch sphere dynamics (Sec. 8.5- SCH) ·
Energy
time uncertainty relation (Sec. 2.1-SAK) ·
Heisenberg
representation and the Heisenberg equation of motion (Sec. 2.2 - SAK) |
|
Week
7 |
|
|
Monday,
October 12 |
·
Ehrenfest theorem (Sec. 2.2-SAK) |
|
Wednesday,
October 14 |
·
Simple
Harmonic oscillator (Sec 2.3 -SAK) |
|
Friday,
October 16 |
·
Schrodinger
wave-equation (Sec. 2.4. SAK) |
|
Week
8 |
|
|
Monday,
October 19 |
·
Classical
limit/Bohmian mechanics (Sec. 2.4 - SAK) ·
Semiclassical WKB approximation (Sec. 2.5-SAK) |
|
Wednesday,
October 21 |
·
WKB
connection formula/bound states |
|
Friday,
October 24 |
·
Propagator of the Schrodinger equation (
Sec. 2.6 - SAK) |
|
Week
9 |
|
|
Monday,
October 27 |
·
Path
integral (Sec 2.6 - SAK) |
|
Wednesday,
October 29 |
·
Constant
potentials and Neutron interferometery using path
integrals- (Sec 2.7 of SAK) |
|
Friday,
October 31 |
·
Hamiltonian
Schrodinger equation for a charged particle in a B field – Landau levels (Sec
2.7 - SAK) |
|
Week
10 |
|
|
Monday,
November 3 |
·
Lagrangian for the charged particle; diamagnetism of a
superconductor ·
Particle
in a ring |
|
Wednesday,
November 5 |
·
Gauge
invariance in wave-function and bra-ket notation
(Sec. 2.7-SAK) ·
Vector
potential in the action formalism and path-integral. |
|
Friday,
November 7 |
·
Aharonov-Bohm effect using
the path integral formalism (2.7 SAK) |
|
Week
11 |
|
|
Monday,
November 9 |
·
Discuss
midterm |
|
Wednesday,
November 11 |
·
Rotations
as a non-abelian group and commutators of angular momentum (Sec. 3.1 of SAK) |
|
Friday,
November 13 |
·
Extra
- sign from 2pi rotations for spin-1/2 particles (Sec. 3.2 - SAK) ·
Euler
angle representation of rotations |
|
Week
12 |
|
|
Monday,
November 16 |
·
Eigenvalues
and Eigenvectors of the angular momentum operators (Sec. 3.5.- SAK) |
|
Wednesday,
November 18 |
·
Orbital
angular momentum & the angular momentum algebra (Sec 3.6-SAK). |
|
Friday,
November 20 |
·
Spherical
harmonics (Sec. 3.7-SAK) ·
Schrodinger
equation in rotationally symmetric potentials (Sec 3.7-SAK) – radial schrodinger equation |
|
Week
13 |
|
|
Monday,
November 23 |
·
Radial
Schrodinger equation – mapping to 1D, boundary conditions – special cases
Spherical well, Hydrogen atom, 3D Harmonic oscillator (Sec 3.7-SAK) |
|
Wednesday,
November 25 |
·
Schrodinger
equation for the 3D Harmonic oscillator from angular momentum algebra |
|
Friday,
November 28 |
Thanksgiving
Holiday, no lecture |
|
Week
14 |
|
|
Monday,
November 30 |
·
Addition
of angular momentum (Sec 3.8 - SAK) – pair of spin-1/2, ·
Addition
of orbital/spin angular momentum (Sec. 3.8 - SAK) |
|
Wednesday,
December 2 |
·
Clebsch-Gordon recursion relations (Sec. 3.8 - SAK) |
|
Friday,
December 4 |
·
Schwinger’s
oscillator model for angular momentum (3.9 SAK) ·
Cartesian
and spherical tensor operators (Sec. 3.11 - SAK) |
|
Week
15 |
|
|
Monday,
December 7 |
·
State
and prove Wigner-Eckart theorem |
|
Wednesday,
December 9 update point |
·
Example
of application of Wigner-Eckart |
|
Friday,
December 11 (lecture
skipped) |
·
Parity
symmetry and its violation (Sec. 4.2 - SAK). ·
Time
reversal symmetry and Kramers
theorem (Sec. 4.4 -SAK). |
|
Final
Exam |
|
|
Wednesday
Dec 2 from 12pm to Monday Dec 6 11am. |
|
Last updated September 2, 2014