Download Chemistry 521/421 Fall 2013 Atomic and Molecular Structure

Chemistry 521/421
Fall 2013
Atomic and Molecular Structure (Elements of Quantum Mechanics)
Course description:
This is a theoretical course designed to provide a thorough introduction to quantum mechanics in
chemistry, and is suitable for graduate students and advanced undergraduate students. The focus
of the course will be on fundamentals, emphasizing use of the Heisenberg-Dirac representations.
Dirac notation will be used from the beginning, and the use of raising and lowering operators for
oscillators, matter-radiation interactions, and angular momentum will be emphasized.
Instructor: Prof. Ed Castner, WL-184, [email protected]
Lectures: Tuesdays and Thursdays, 5:00-6:20
Location: WL-260
Required Text: Elements of Quantum Mechanics, by Michael D. Fayer
Oxford University Press, 2001, ISBN 0-19-514195-4
www.us.oup.com/us/catalog/general/subject/Chemistry/MaterialsChemistry/?view=usa&ci=0195141954
(text available at Rutgers Bookstore, New Brunswick)
Supplemental Texts:
The ideal texts for students to learn more about quantum mechanics include the classics
by Dirac, "Principles of Quantum Mechanics" (4th ed., Oxford University Press), and by CohenTannoudji, Diu, and Laloë, "Quantum Mechanics" (Wiley).
Though not required, the following text and its solutions manual may be helpful to the
student looking to learn quantum mechanics from more than one perspective, and has the
advantage of making a detailed solutions manual available for working examples.
P. W. Atkins and R. S. Friedman, Molecular Quantum Mechanics, Oxford Univ. Press and
P. W. Atkins and R. S. Friedman, Solutions Manual for Molecular Quantum Mechanics.
Homework Assignments:
In general, the homework is to work each of the problems in the Fayer text, Elements of
Quantum Mechanics. Note that the problems are found at the end of the book, pp. 295-313,
_not_ at the end of each chapter. Homework will not be graded, but you must do all of the
assigned homework problems on time to keep up with the course material. Answers to the
problem sets will be posted on week after each assignment on the course Sakai site.
These homework problems are challenging. I strongly urge students to work together and form
study groups for working the problems.
Course prerequisites:
Students must have had an introductory course in physical chemistry at the level of Rutgers
Chemistry 01:160:328, with quantum mechanics treated at a level equivalent to that covered in
"Physical Chemistry: A Molecular Approach" by McQuarrie and Simon or in "Physical
Chemistry" by Reid and Engel. An understanding of the material from undergraduate physics
courses is also required, including electromagnetism and modern physics. A strong mathematical
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background is required, including but not limited to linear algebra, differential equations, and
multi-dimensional calculus. All mathematical constructs and concepts will be defined, but
students should have had prior exposure to the material. A list of such topics is given below.
Prerequisite knowledge and background for Chem. 521/421:
Students should have previously been exposed to the concepts below. Please survey your
previous texts and lecture notes _before_ the start of the course to refresh your memory on any
subjects you feel uncertain of. Each of these elements will be defined during the course, but
some prior knowledge is expected.
Blackbody radiation, Planck law, and Einstein's description of the photoelectric effect
deBroglie wavelengths and matter waves; Heisenberg Uncertainty Principle; conjugate variables
Rydberg formula for H atom via the Bohr theory
Schrödinger equation
free particle wavefunctions; particles in an infinite potential well in 1, 2, and 3 dimensions
matrix elements for observable linear operators
linear and angular momentum
the six postulates of quantum mechanics
Hamiltonian formulation of total system energy
classical and quantum harmonic oscillators- reduced mass; the zero point energy
rigid rotators
hydrogen-like atom wavefunctions
linear combinations of atomic orbitals to form molecular orbitals.
transition dipole matrix elements and selection rules for quantum transitions
simultaneous observables; allowed quantum numbers
approximation methods: variational and perturbation theories
multi-electron atoms; the Hartree-Fock self-consistent field method
the electron spin hypothesis; Hund's rules
chemical bonding- covalent, ionic, weak van der Waals and hydrogen bonds
ground and excited electronic states of atoms and molecules
Mathematics
complex numbers
spherical and polar coordinates
vectors and vector linear spaces: scalar and cross products, projections
linear algebra- matrix arithmetic, inversion, determinants
solving systems of equations
Hermitian (or self-adjoint) operators; unitary operators
commutators and anti-commutators
wave equation- classical harmonic oscillators
differential equations: separation of variables, non-linear equations.
special functions: Legendre, Laguerre, Hermite, and spherical harmonics
statistics and probability distributions- Gaussian and otherwise
linear operators; eigenvalue equations, eigenvalues
Fourier transformations
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