Offered: jointly with GWSS Written and oral presentations summarizing work accomplished are required. PHYS Mechanics 3 Lagrangian and Hamiltonian dynamics, with applications to various topics such as coupled oscillators, parametric resonance, anharmonic oscillations, chaos. PHYS Numerical Methods 3 Integration, solution of differential equations, Monte Carlo methods, function minimization, data analysis, modern computing techniques, computation in experimental physics. PHYS Physical Applications of Group Theory 3 Applications of finite and continuous groups, representation theory, symmetry, and conservation laws to physical systems.

Principles of electrostatics, complex variable techniques, boundary value problems and their associated mathematical techniques, Green's functions.

Electric and magnetic fields in free space and material media, wave guides and cavity resonators. Special relativity, electromagnetic radiation from accelerated charges, synchrotron radiation, Cerenkov radiation, radiation reaction. Modern non-relativistic quantum mechanics developed, beginning with its basic principles. Dirac and abstract operator notation introduced, starting with simple examples. Modern non-relativistic quantum mechanics. The character of the theory illustrated both with physical examples and with conceptual problems. Topics include: atomic structure, scattering processes, density operator description of mixed states, and measurement theory.

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Abstract operator methods emphasized in the exposition of angular momentum, scattering, and perturbation theory. Physical examples and conceptual problems. PHYS Advanced Quantum Mechanics - Introduction to Quantum Field Theory 4 Multi-particle systems, second quantization, diagrammatic perturbation theory, radiation, correlation functions and multi-particle scattering, relativistic theories, renormalizability, basic quantum electrodynamics, and other applications.

PHYS Advanced Quantum Mechanics - Introduction to Quantum Field Theory 3 Multi-particle systems, second quantization, diagrammatic perturbation theory, radiation, correlation functions and multi-particle scattering, relativistic theories, renormalizability, basic quantum electrodynamics, and other applications.

## Graduate programs in physics at HRI

PHYS Thermodynamics and Statistical Mechanics 4 Statistical mechanical basis of the fundamental thermodynamical laws and concepts; classical and quantum statistical distribution functions; applications to selected thermodynamic processes and examples of Bose and Fermi statistics. PHYS Statistical Mechanics 3 Introduction to equilibrium and non-equilibrium aspects of many-body systems; scale invariance and universality at phase transitions and critical phenomena; exactly soluble models; Markov processes, master equations and Langevin equation in non-equilibrium stochastic processes.

Topics may include continuous and pulsed lasers; solid, liquid, and gas gain media; Q-switching, mode-locking, resonator theory, nonlinear optics, and others. Prerequisite: basic quantum mechanics, electromagnetism, and optics. Phases, phase transitions, optical and dielectric properties, molecular and device "engineering," future prospects.

PHYS Introduction to Acoustics and Digital Signal Processing 4 Introduces mathematical and physics principles of acoustics in digital signal processing applications. Complex analysis and Fourier methods, physics of vibrations and waves, solutions of the wave equation, digital convolution and correlation methods, and Maximum Length Sequence method in signal analysis and spread-spectrum applications. PHYS Applications of Quantum Physics 4 Techniques of quantum mechanics applied to lasers, quantum electronics, solids, and surfaces.

Emphasis on approximation methods and interaction of electromagnetic radiation with matter. Topics may include integration, differential equations, partial differential equations, optimization, data handling, and Monte Carlo techniques.

Emphasis is applications in physics. Prerequisite: 30 credits in physical sciences, computer science, or engineering. Static electric and magnetic fields. Boundary-value problems. Electric and magnetic properties of materials. Electromagnetic waves and radiation. Topics may include electromagnetic waves, radiation, scattering, wave guides, plasma physics, quantum electronics, and accelerator physics. Prerequisite: PHYS or equivalent.

Subjects include Fourier optics, lens systems, interferometry, laser optics, holography, polarization, crystal optics, birefringence, laser and conventional light sources, optical detectors. PHYS Condensed-Matter Physics 4 Introduction to the theory of solids: crystal structure in real space and reciprocal space, phonons, free electrons, band theory, semiconductor devices.

### Scattering theory in quantum mechanics : physical principles and mathematical methods

Topics include noise, control-system analysis, operational amplifiers, lock-in amplifiers, precision power supplies and metering, data transmission, microprocessors. Several integrated measurement systems are examined in the context of specific research problems. Prerequisite: elementary electronics. The topics include advanced calculus, series, matrix, complex variables, and differential equations.

## Condensed matter physics

The topics include special functions, integral transforms, variational techniques, integral equations. In addition, students performs experiments, which made significant contribution in developing modern physics. They acquire ability for constructing electric circuits and operating skill for electronic equipments through this course.

Also applications of electromagnetic waves to modern technologies will be introduced. It is impossible, however, to find all microscopic states exactly due to the complexity of many body systems. We thus study Statistical Thermal Physics to find and understand the average behaviors and properties, starting from a probabilistic point of view not a deterministic one. Microscopic world is explored in nonrelativistic region.

### Course structure

Topics to be covered include the Schroedinger equation on the matter waves, basic structure of the quantum mechanics, bound state problems in one and three dimensional spaces. Items related to Scattering theory in quantum mechanics: Physical principles Scattering theory in quantum mechanics: Physical principles and mathematical methods Lecture notes and supplements in physics ; Werner O Amrein.

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