Vector and tensor fields and transformation properties under rotation of axes, vector identities, gradient, divergence, curl, tensor contraction, geometric interpretation of symmetric and antisymmetric tensors, divergence-Gauss' theorem for tensor fields and Stokes' theorem, Helmholtz' theorem, and scalar and vector potentials. Applications to inertia tensor, particle mechanics, transport, electromagnetism (Maxwell's equations), and viscous fluid dynamics (the Navier-Stokes equation, Euler equation, and the Bernoulli equation). Introduction to the Dirac delta-function and Green?s function technique for solving linear inhomogeneous equations. Orthogonal curvilinear coordinates (general, also spherical, and cylindrical). N-dimensional complex space and unitarity, matrix notation, inverse of matrix, Pauli spin matrices, relativity, and Lorentz transformation. Tensors and pseudotensors in n-dimensions. Similarity transformations and diagonalization of Hermitian and unitary matrices, eigenvectors, and eigenvalues of Hermitian and unitary matrices, and Schmidt orthogonalization. Applications to coupled oscillators, rigid body dynamics, etc. Linear independence and completeness. Functions of a complex variable, analyticity, Cauchy?s theorem, Residue theorem, Taylor and Laurent expansions, classification of singularities, analytic continuation, Liouville?s theorem, multiple-valued functions, contour integration, Jordan?s lemma, applications, and asymptotics. Fall Semester.
Particle motion in one dimension. Simple harmonic oscillators. Motion in two and three dimensions, kinematics, work and energy, conservative forces, central forces, and scattering. Systems of particles, linear and angular momentum theorems, collisions, linear spring systems, and normal modes. Lagrange’s equations and applications to simple systems. Introduction to moment of inertia tensor and to Hamilton’s equations.
Ordinary differential equations of first and second order, homogeneous and non-homogeneous equations; improper integrals, Laplace transforms; review of infinite series, series solutions of ordinary differential equations near an ordinary point; boundary-value problems; orthogonal functions; Fourier series; separation of variables for partial differential equations. Close
Particle motion in one dimension. Simple harmonic oscillators. Motion in two and three dimensions, kinematics, work and energy, conservative forces, central forces, scattering. Systems of particles, linear and angular momentum theorems, collisions, linear spring systems, normal modes. Lagrange's equations, applications to simple systems. Introduction to moment of inertia tensor and to Hamilton's equations Close
Ordinary differential equations of first and second order, homogeneous and non-homogeneous equations; improper integrals, Laplace transforms; review of infinite series, series solutions of ordinary differential equations near an ordinary point; boundary-value problems; orthogonal functions; Fourier series; separation of variables for partial differential equations. Close
The general study of field phenomena; scalar and vector fields and waves; dispersion phase and group velocity; interference, diffraction and polarization; coherence and correlation; geometric and physical optics. Typical text: Hecht and Zajac, Optics. Spring semester.
This course is designed to make students comfortable with the handling and use of various optical components, instruments, techniques,and applications. Included will be the characterization of lens, wavefront division and multiple beam interferometry, partial coherence, spectrophotometry,coherent propogation, and properties of optical fibers.
The general study of field phenomena; scalar and vector fields and waves; dispersion phase and group velocity; interference, diffraction and polarization; coherence and correlation; geometric and physical optics. Typical text: Hecht and Zajac, Optics. Spring semester. Close
This course is meant to serve as an introduction to formal quantum mechanics as well as to apply the basic formalism to several generic and important applications.
Ordinary differential equations of first and second order, homogeneous and non-homogeneous equations; improper integrals, Laplace transforms; review of infinite series, series solutions of ordinary differential equations near an ordinary point; boundary-value problems; orthogonal functions; Fourier series; separation of variables for partial differential equations. Close
Simple harmonic motion, oscillations and pendulums; Fourier analysis; wave properties; wave-particle dualism; the Schrödinger equation and its interpretation; wave functions; the Heisenberg uncertainty principle; quantum mechanical tunneling and application; quantum mechanics of a particle in a "box," the hydrogen atom; electronic spin; properties of many electron atoms; atomic spectra; principles of lasers and applications; electrons in solids; conductors and semiconductors; the n-p junction and the transistor; properties of atomic nuclei; radioactivity; fusion and fission.
The course is designed to familiarize students with a range of optical instruments and their applications. Included will be the measurement of aberrations in optical systems, thin-film properties, Fourier transform imaging systems, nonlinear optics, and laser beam dynamics.
Fall term. This course may sometimes be offered in the spring term if space
The general study of field phenomena; scalar and vector fields and waves; dispersion phase and group velocity; interference, diffraction and polarization; coherence and correlation; geometric and physical optics. Typical text: Hecht and Zajac, Optics. Spring semester. Close
An introductory course to the theory of lasers; treatment of spontaneous and stimulated emission, atomic rate equations, laser oscillation conditions, power output, and optimum output coupling; CW and pulsed operation, Q switching, mode selection, and frequency stabilization; excitation of lasers, inversion mechanisms, and typical efficiencies; detailed examination of principal types of lasers, gaseous, solid state, and liquid; and chemical lasers, dye lasers, Raman lasers, high power lasers, TEA lasers, and gas dynamic lasers. Design considerations for GaAlAs, argon ion, helium neon, carbon dioxide, neodymium YAG, and pulsed ruby lasers. Fall semester. Typical text: Yariv, Optical Electronics.
This course is designed to make students comfortable with the handling and use of various optical components, instruments, techniques,and applications. Included will be the characterization of lens, wavefront division and multiple beam interferometry, partial coherence, spectrophotometry,coherent propogation, and properties of optical fibers.
Basic concepts of quantum mechanics, states, operators; time development of Schrödinger and Heisenberg pictures; representation theory; symmetries; perturbation theory; systems of identical particles, L-S and j-j coupling; fine and hyperfine structure; scattering theory; molecular structure.
Particle motion in one dimension. Simple harmonic oscillators. Motion in two and three dimensions, kinematics, work and energy, conservative forces, central forces, and scattering. Systems of particles, linear and angular momentum theorems, collisions, linear spring systems, and normal modes. Lagrange’s equations and applications to simple systems. Introduction to moment of inertia tensor and to Hamilton’s equations. Close
Quantum Mechanics and Engineering Applications (3-0-6)
(Lecture-Lab-Study Hours)
This course is meant to serve as an introduction to formal quantum mechanics as well as to apply the basic formalism to several generic and important applications. Close
Integrated optics, nonlinear optics, Pockels effect, Kerr effect, harmonic generation, parametric devices, phase conjugate mirrors, and phase matching. Coherent and incoherent detection, Fourier optics, image processing and holography, and Gaussian optics. Detection of light, signal to noise, PIN and APD diodes, and optical communication. Scattering of light, Rayleigh, Mie, Brillouin, Raman, and Doppler shift scattering. Spring semester.
