Quantum
Mechanics - I, Fall 2009
Time: Mon. 10:10-12:00, Wed.
9:00-9:50
Classroom:
Room 019, Physics
Lecturer: We-Fu Chang (張維甫)
e-mail: < wfchang_AT_phys_nthu_edu_tw >
Room618, ext 31111
Office Hour: by appointment.
Tutorial section: Tue. and Fri. 7:00pm-8:00pm
Prerequisite:
本課程適合大四（含）以上，修過量子物理同學選修.
You are expected to have the basic quantum mechanics knowledge at
the level of
D.J. Griffiths, Introduction
to Quantum Mechanics, 2nd Edition.
Textbook: J.J. Sakurai, Modern
Quantum Mechanics, Revised Edition.
Recommedned References
Grading Policy:
50% Homework 
,
20%
Midterm 
,
30%
Final 
,
Score
TA: 劉嘯青 潘維平(
Room 606, ext 62443 ) 林冠君
(Room, ext 33314 )
Discuss with the TA if you have any question about your homework
grading.
Homework:
( 注意: 不收遲交作業, 對抄襲或作弊零容忍 )
Doing
the
problem sets is an extremely important part of learning. You can't
learn the subject by just listening to the lectures without working
through things by yourself. They also contain some of the important
topics that we won't be able to cover in class. You can discuss the
problem
sets with your classmates, but you are not allowed to copy other
people's homework.
Each of you is required to write up your own homework following your
own understandings.
Each problem set is due about one week after its assignment in class.
The solutions will be given on this website immediately
after the class on the due day and hence late submition
will not be accepted.
So even if you couldn't finish you
should turn in
what you have done.
You should summit the HW to the TA's ahead of the deadline if for some
reason you
can't attend the class on the due day.
The following homework solutions are provided by TA.
Course Log:
- Sep.14:
Hilbert Space, Dual Correspondence, Dirac bra and ket,
scalar product.
- Sep.16:
Hermitian Conjugate, Linear operator, Completness.
- Sep.21:
Direct sum, More on Completeness(mixed spectrum),
theorem on two commuting operators and simultaneous eigenbasis,
projection operator, function of an observable.
- Sep.23:
Matrix representation, some Math tricks involving Trace,
det, and exp. First exposure to the postulates of QM.
- Sep.28(no class due to teacher's day), Sep.30: Lecturer is out of
town for ICFP09, TA time
- Oct.5:
Construct the corrosponding Hilbert space, operators, eigenbasis solely
from the postulates of QM and the outcomes of Stern-Gerlach exp,
Complete set of commuting observables, average and deviation of a
measurement, generalized uncertainty principle.
- Oct.7:
Density operator
- Oct.12:
More on density operator, connection to statistical Mechanics, entropy,
pure/mixed states, revised postulates of QM.
- Oct.14:
EPR paradox, Bell's inequality (closely follow Sakurai's
Sec. 3.9 )
- Oct
19: Direct Product(see Shankar, p256-), D.
Mermins's simple
demonstration on the difference between QM and hidden variable
theories, brief introduction to Sydney Coleman's lecture, view the clip,
final remarks on the postulates of QM.
- Oct.21:
(see Sakurai 1.6-1.7) Configuratin representation; position
operator, wave function, translation operator.
- Oct.26:
(see Sakurai 1.6-1.7) Kinetic and canonical momentum, generator
for translation in CM and QM, momentum operator in QM, in configuration
representation.
- Oct.28:
(see Shankar QM chap.2, and Landau, Mechanics Chap.7 ) 1hr
review of the classical mechanics.
- Nov.2:
(see Sakurai 2.1) Time evolution in QM, Heisenberg and Schrodinger
picture, time evolution of the density operator.
- Nov.4:
initial value problem, Schrodinger equation, probablility density and
current, classical limit
- Nov.9:
The Ehrenfest relation, particle in EM background, gauge transformation
in QM, some properties of 1D Schrodinger Eq: Degeneracies, Reality, and
Nodes interleaving.
- Nov.11:
Simple 1D problems
- Nov.16:
Midterm
(期中考), Solution
10:10 am -12:00, Nov.19:
No class due to universitysport game
- Nov.23: No class due to sick leave,
Nov.25: Quantum beat
- Nov.30:
WKB approximation, Steepest descent approximation
- Dec.2:
Numerical method for 1D problem, 1D Simple Harmonic Oscillator
- Dec.
7,9:
1D SHO, coherent states, (check the online JAVA program ),
squeezed states
- Dec.
9: Path Integral (Prelude)
- Dec.
14: Path Integral: derivation,matrix element of operators,
Euler-Lagrangian Eq, Schrodinger Eq, and partition function from PI
- Dec.
16: position dependent potential,Aharonov-Bohm effect, magnetic
monopole
- Dec.
21, 23: Rotation group, angular
momentum operators, commutation relations, properties of the angular
momentum operators, rotation matrices and representtions
- Dec.
28: j=1/2 particle in const
magnetic field (demonstartion clip),
Lande g-factor, magnetic
resonance, NMR and MRI( transition
prob ).
- Dec.
30: Orbital Angular Momentum, spherical harmonics.
- Jan.
4: Addition of angular momentum, the Clebsch-Gordan coefficients (PDG
link).
- Jan.
6: some properties of wave mechanics in 3D
- Jan. 11: Final
(期末考), Solution
10:10
am -12:00, OPEN BOOK
hits
since Oct.14, 2009
Port
Macquarie Accommodation