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Quantum
Mechanics 171.605 Fall 2009
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This is the
first 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 the latest advances in medical technology to the rise of
trillion dollar computer & communication industries to laptops, iPods,
quantum computing 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 theory, (Second semester) Coulomb and resonant
scattering, spin, density matrix, entangled states and quantum
information, perturbation theory (time-independent and
time-dependent), quantized radiation field, absorption and emission of
radiation, 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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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 the final grade. The homeworks
will be distributed on the day of the conference, and will be due the
following week. No late homework will be accepted! There will be a
closed book midterm exam in late October/early November, 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 convincingly better
than 1,000 points total to receive a passing grade (for example, 800
points on homeworks and 210 on exams does not
qualify for a pass).
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Homeworks
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Homeworks
are due at the start of each 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 : Tuesdays and Thursdays, 10:30 – 11:45 am,
Bloomberg 278
Conference: Fridays, 12:00 – 12:50 pm, Bloomberg 361
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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). Older
editions of Schwabl’s book will serve just
fine.
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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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