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 2013. 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 |
|
|
Wednesday,
September 3 |
·
History
of quantum mechanics - Raleigh-Jean's paradox, Planck's radiation law, Photo
electric effect (photons) ·
Wave-particle
duality (Sec. 1.2 - SCH) ·
Photon
interferometers, (Sec. 2.1 - SCH) |
|
Friday,
September 5 |
·
complex
amplitudes, beam splitters, matrix methods, testing bombs (Sec. 2.1 - SCH) |
|
Week
2 |
|
|
Monday,
September 8 |
·
Particles
with spin-1/2, Stern Gerlach, bras-kets, measurements and filters (Sec. 2.2-SCH) |
|
Wednesday,
September 10 |
·
Preliminary
energy spectrum and time evolution, operators, spins (Sec. 2.3-SCH) |
|
Friday,
September 12 |
·
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) |
|
Wednesday,
September 17 |
·
Adjoints - hermitean, positive, anti-hermitean, unitary, normal operators (Sec. 3.4- SCH) ·
Eigenvalues
and Eigenvectors. (Sec. 3.5 - SCH) |
|
Friday,
September 19 |
·
Degeneracy
and commuting observables (Sec. 3.5-SCH) |
|
Week
4 |
|
|
Monday,
September 22 |
·
Continuous
Hilbert space, position, translations and momenta (Sec 1.6, SAK) |
|
Wednesday,
September 24 |
·
Wave-functions
in position space (Sec. 1.7 SAK) |
|
Friday,
September 26 |
·
Wave-functions
in momentum space (Sec. 1.7 SAK) ·
Wave
-packets (Sec. 1.7 SAK) ·
Heisenberg
Uncertainty relation (Sec. 4.5 - SCH) ·
Quantum
cryptography (Sec. 4.4 - SCH) |
|
Week
5 |
|
|
Monday,
September 29 |
·
Composite
systems (Sec. 6.1 - SCH) |
|
Wednesday,
October 1 |
·
Interaction
and Entanglement (Sec. 6.2-SCH) ·
EPR
paradox - local hidden variables (Sec. 6.5 - SCH) |
|
Friday,
October 3 |
·
GHZ
states version of Bell’s inequality (Sec. 6.7 - SCH) ·
Quantum
versus classical uncertainty, density operators (Sec. 8.1 - SCH) |
|
Week
6 |
|
|
Monday,
October 6 |
·
Bloch
sphere (Sec. 8.4- SCH) ·
Canonical
ensembles and von Neumann entropy (Sec. 8.6,8.6-SCH) ·
Entanglement
entropy |
|
Wednesday,
October 8 |
·
The
Schrodinger equation for the time evolution operator (Sec 2.1 -SAK) ·
Energy
Eigenkets, time dependence of expectation values |
|
Friday,
October 10 |
·
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 13 |
·
Ehrenfest theorem (Sec. 2.2-SAK) |
|
Wednesday,
October 15 |
·
Simple
Harmonic oscillator (Sec 2.3 -SAK) |
|
Friday,
October 17 |
·
Schrodinger
wave-equation (Sec. 2.4. SAK) |
|
Week
8 |
|
|
Monday,
October 20 |
·
Classical
limit (Sec. 2.4 - SAK) |
|
Wednesday,
October 22 |
·
Semiclassical WKB approximation ·
Sec
2.5 (excluding the linear potential and the Harmonic oscillator). |
|
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 (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 ·
Dirac's
magnetic monopole for the quantization of charges (Sec 2.7. from SAK). ·
Rotations
as a non-abelian group and commutators of angular momentum (Sec. 3.1 of SAK) |
|
Week
11 |
|
|
Monday,
November 10 |
·
Extra
- sign from 2pi rotations for spin-1/2 particles (Sec. 3.2 - SAK) ·
SU(2)
as a double cover of SO(3) (Sec. 3.3.- SAK) |
|
Wednesday,
November 12 |
·
Euler
angle representation of rotations |
|
Friday,
November 14 |
·
Eigenvalues
and Eigenvectors of the angular momentum operators (Sec. 3.5.- SAK) ·
Orbital
angular momentum as that obey the angular momentum
algebra and Spherical harmonics (Sec 3.6-SAK). |
|
Week
12 |
|
|
Monday,
November 17 |
·
Schrodinger
equation in rotationally symmetric potentials (Sec 3.7-SAK). |
|
Wednesday,
November 19 |
·
Schrodinger equation for spherical well (Sec.
3.7-SAK) |
|
Friday,
November 21 |
·
Schrodinger
equation for the 3D Harmonic oscillator using power series |
|
Week
13 |
|
|
Monday,
November 24 |
·
Coulomb
potential using the SO(4) solution (Sec. 4.1 -SAK). |
|
Wednesday,
November 26 |
·
Addition
of angular momentum (Sec 3.8 - SAK) – hydrogen atom |
|
Friday,
November 28 |
Thanksgiving
Holiday, no lecture |
|
Week
14 |
|
|
Monday,
December 1 update point |
·
Addition
of angular momentum (Sec 3.8 - SAK) – pair of spin-1/2 ·
Clebsch-Gordon coefficients (Sec. 3.8 - SAK) |
|
Wednesday,
December 3 |
·
Clebsch-Gordon recursion relations (Sec. 3.8 - SAK) ·
Symmetry
and conservation law (Sec. 4.1 - SAK) ·
Parity
symmetry and its violation (Sec. 4.2 - SAK). ·
Discrete
symmetry ( with translational symmetry as example) (Sec. 4.3 -SAK) |
|
Friday,
December 5 |
·
Schwinger’s
oscillator model for angular momentum (3.9 SAK) |
|
Week
15 |
|
|
Monday,
December 8 |
·
Cartesian
and spherical tensor operators (Sec. 3.11 - SAK) |
|
Wednesday,
December 10 |
·
State
and prove Wigner-Eckart theorem |
|
Friday,
December 12 |
·
Time
reversal symmetry and Kramers
theorem (Sec. 4.4 -SAK). |
|
Final
Exam |
|
|
Thursday,
December 18, 8-10 am |
|
Last updated September 2, 2014