Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
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 1 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 2