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Quantum Mechanics
171.606 Spring 2008
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This is the
second part of a two-semester graduate level course in quantum mechanics.
Arguably, the quantum theory represents the finest intellectual
achievement of modern science. Its predictions are as profound as they
are bewildering -- our "common sense" intuition is frequently
overwhelmed when faced with its many paradoxes. Yet, the combined power
of its logical, mathematical structure and numerous experimental
validations force us to accept quantum mechanics as our basic theory of
the physical universe -- it is the most quantitatively accurate theory in
physics and its myriad of applications influence every aspect of modern
life, from latest advances in medical technology to rise of trillion
dollar computer/communication industries to laptops, iPods
and the like. After this two-semester course, a graduate student will be
equipped with solid conceptual and practical understanding of quantum
theory and be able to start gaining a foothold on the contemporary
research frontier in physical sciences.
In lieu of
Syllabus, sampling of
topics to be covered: (First semester) review of the wave mechanics and
the Schrödinger equation, Hilbert space and quantum operators, harmonic
oscillator, coherent states, equations of motion for operators, the WKB approximation, central forces and angular momentum,
scattering, (Second semester) Coulomb and resonant scattering,
perturbation theory (stationary and
time-dependent), quantized radiation field, absorption and emission of
radiation, spin, density matrix, entangled states and quantum information,
identical particles, second quantization and quantum many-body
problem, Dirac equation and relativistic quantum mechanics.
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Class announcements:
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Midterm
Exam
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Friday, March 28
12:00 - 1:15 pm, Bloomberg 361
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Final
Exam
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Exams and grading
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During the semester there will be weekly homeworks each carrying 100 points. Out of
these, 8 on which you scored the most points will be included in the
computation of final grade. The homeworks will
be distributed on the day of the class/conference, and will be due the
following week. No late homework will be accepted! There will be a
closed book midterm exam in late March/early April, worth
400 points. At the end of the semester there will be a final exam,
worth 800 points. Your grade will be decided on the basis of total number
of points from homeworks, midterm and final
exam. Graduate students are generally expected to do better than 1,000
points total to receive a passing grade.
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Homeworks
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Homeworks
are due at the start of each class/conference, one week after being posted. The
problems will be posted on this page in Adobe Portable
Document Format (*.pdf). PDF is the preferred
format for viewing documents on screen.
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Class hours and Location
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Lectures : Thursdays, 10:30 – 11:45 am
(Bloomberg 278); Fridays, 12:00 noon – 1:15 pm (Bloomberg 361)
Conference: Tuesdays, 10:30 - 11:20 am (Bloomberg 278)
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Lecturer and TA info
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Textbooks and related links
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Primary textbook:
“Quantum Mechanics” by F. Schwabl
(Springer) offers a solid and comprehensive introduction to the subject
and perhaps is the closest in style and emphasis to the lectures. Toward the end of the Spring semester, we will also discuss subjects covered in the second part of
Schwabl's treatise, the “Advanced Quantum Mechanics” (Springer).
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Other useful
textbooks and www links: There are at least ten good textbooks
on quantum mechanics. The formidable classics are Landau & Lifshitz, Davydov,
Messiah, Schiff and Baym. The modern
standouts are Shankar and Sakurai. Cohen-Tannoudji,
Diu & Laloe “Quantum
Mechanics” (Wiley) is beloved by students for its step-by-step
style, R. Robinett’s “Quantum
Mechanics” (Oxford) has many contemporary physics examples, A. Bohm’s “Quantum Mechanics; Foundations
and Applications” (Springer) is heavy on mathematical rigor, R. Omnes’ “The Interpretation of Quantum
Mechanics” (Princeton University Press) dwells on the conceptual
side, while the good old S. Flugge’s
“Practical Quantum Mechanics” (Springer) still separates
the men/women from the boys/girls.
There are also numerous useful web links on various aspects of quantum
theory. A sampling (many in the form of Java applets) includes a 1D
Quantum Crystal, Curious
world of quantum by Prof. M. Franz from UBC, Quantum Physics
Online from French Ecole Polytechnique, Visual Quantum
Mechanics from Kansas State, 1D
Quantum Mechanics by Paul Falstad, etc.
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