- Classical Mechanics
The graduate course in advanced Classical Mechanics explores the fundamental principles and mathematical formalism underlying classical mechanics. Building upon the foundational concepts covered in undergraduate physics, this course aims to provide students with a comprehensive understanding of classical mechanics at an advanced level. The course begins with a review of Newtonian mechanics, including the principles of motion, forces, and conservation laws. Special attention is given to the concepts of generalized coordinates, Lagrangian mechanics, and Hamiltonian mechanics. The Lagrangian and Hamiltonian formulations serve as powerful tools to analyze the dynamics of complex systems and enable the exploration of a wide range of physical phenomena. (4 credits)
- Electromagnetism
The graduate course in advanced Electromagnetism discusses electromagnetic theory, covering both classical and modern aspects of the subject. This course aims to deepen students’ understanding of the fundamental principles and mathematical formalism underlying electromagnetism, and their ability to apply this knowledge to solve complex problems in the field. The course begins with a review of Maxwell’s equations, providing a comprehensive understanding of the laws governing electric and magnetic fields. Special attention is given to the vector calculus and mathematical techniques necessary for analyzing electromagnetic phenomena.
Topics include electrostatics (Coulomb’s law and Gauss’s law, electric potential and energy, conductors, semiconductors, and insulators, with special attention to capacitors and dielectrics), magnetostatics (Biot-Savart law and Ampere’s law, magnetic materials and boundary value problems, magnetic vector potential, and magnetic forces and torque), electrodynamics (Faraday’s law, Maxwell’s equations in integral and differential forms, electromagnetic waves and propagation), electromagnetic radiation, electromagnetic wave interactions with matter, as well as relativistic electrodynamics and covariant formulation. (4 credits)
- Quantum Mechanics
This graduate-level course provides a comprehensive exploration of the principles and applications of quantum mechanics, the fundamental theory that governs the behavior of matter and energy at the microscopic scale. Quantum mechanics revolutionized our understanding of the physical world and forms the basis of modern physics. The course begins with a review of the key principles and mathematical formalism of quantum mechanics, including the wave-particle duality, superposition, and the postulates of quantum mechanics. It then delves into the fundamental concepts and mathematical tools necessary for studying quantum systems. Topics include mathematical foundations of quantum mechanics (linear algebra and Hilbert spaces, Dirac notation and bra-ket formalism, operators, observables, and eigenvalue problems), time-independent and time-dependent Schrödinger equations, quantum harmonic oscillator, angular momentum and spin, composite systems and entanglement, identical particles and quantum statistics, measurement theory, apparent collapse of the wave function, and multiple story lines within one universal wholeness (M-SLOW). Attention will also be given to quantum information theory, quantum computing, quantum algorithms, and quantum communication. Throughout the course, an emphasis is placed on understanding the foundational principles of quantum mechanics and their applications across various fields of physics. Students will develop proficiency in solving quantum mechanical problems, analyzing quantum systems, and interpreting experimental results.
This course assumes a strong background in undergraduate physics, including classical mechanics, electromagnetism, and mathematical methods. A solid understanding of linear algebra is necessary. Familiarity with differential equations, complex numbers and calculus of variations is helpful but not mandatory, as the course will provide a review of the relevant mathematical concepts. (4 credits)
- General Relativity
This course provides a comprehensive introduction to the theory of General Relativity, which is one of the pillars of modern physics. General Relativity revolutionized our understanding of gravity and space-time, providing a framework to describe the behavior of massive objects and the structure of the universe. The course begins with a brief overview of special relativity and the principles of general covariance, which form the foundation of General Relativity. It then delves into the mathematics of curved space-time, including tensor calculus and the Einstein field equations. Students will develop a solid understanding of the geometric interpretation of gravity and the concept of gravitational waves.
Topics include principles of general relativity (equivalence principle, covariance and invariance), mathematical tools (tensor calculus, curvature and Riemannian geometry, geodesic equations), Einstein field equations, Energy-momentum tensor, Schwarzschild and Kerr solutions, experimental tests and observations (precession of Mercury’s perihelion, deflection of light, gravitational redshift, time dilation in gravitational fields), black holes and cosmology, and gravitational waves. Throughout the course, emphasis is placed on understanding the physical implications of General Relativity and its applications in astrophysics, cosmology, and high-energy physics. Students will develop the necessary mathematical skills to solve problems in curved space-time and gain insight into the profound consequences of Einstein’s theory. (4 credits)
- Quantum Field Theory I
Quantum Field Theory (QFT) is a powerful framework for describing the fundamental interactions of elementary particles and the dynamics of fields in the quantum realm. This course provides a comprehensive introduction to the theoretical foundations and advanced concepts of quantum field theory. The course begins by reviewing the principles of classical field theory, emphasizing Lagrangian and Hamiltonian formulations, symmetries, and conservation laws. The transition from classical to quantum field theory is explored, introducing the concept of second quantization and the interpretation of fields as operators acting on a quantum state. The course then delves into the quantization of scalar, fermionic, and vector fields, highlighting the methodology of canonical quantization, Feynman path integral formulation, and operator quantization techniques. Special attention is given to the principles of gauge symmetry, and the quantization of gauge theories, such as quantum electrodynamics (QED) and the standard model.
Key topics covered in the course include: canonical quantization of scalar fields (Klein-Gordon equation, creation and annihilation operators, Fock space, and vacuum fluctuations), quantization of fermionic fields (Dirac equation, anticommutation relations, spinors), quantization of gauge fields (Abelian and non-Abelian gauge theories and covariant derivatives), interactions in quantum field theory (Feynman diagrams, scattering amplitudes, perturbation theory, and renormalization), spontaneous symmetry breaking, renormalization group, and quantum field theory in curved spacetime.
Throughout the course, students will develop a solid understanding of the mathematical and conceptual foundations of quantum field theory. They will become familiar with advanced techniques, including Feynman diagrams, loop calculations, and the renormalization group, enabling them to analyze and compute observables in realistic field theories. Successful completion of this course will equip students with the necessary tools to pursue research in high-energy physics, condensed matter physics, or other related fields.
A strong background in classical mechanics, electromagnetism, and quantum mechanics is assumed. (4 credits)
- Quantum Field Theory II
Quantum Field Theory (QFT) is a powerful framework for describing the fundamental interactions of elementary particles and the dynamics of fields in the quantum realm. This course provides a comprehensive introduction to the theoretical foundations and advanced concepts of quantum field theory. The course begins by reviewing the principles of classical field theory, emphasizing Lagrangian and Hamiltonian formulations, symmetries, and conservation laws. The transition from classical to quantum field theory is explored, introducing the concept of second quantization and the interpretation of fields as operators acting on a quantum state. The course then delves into the quantization of scalar, fermionic, and vector fields, highlighting the methodology of canonical quantization, Feynman path integral formulation, and operator quantization techniques. Special attention is given to the principles of gauge symmetry, and the quantization of gauge theories, such as quantum electrodynamics (QED) and the standard model.
Key topics covered in the course include: canonical quantization of scalar fields (Klein-Gordon equation, creation and annihilation operators, Fock space, and vacuum fluctuations), quantization of fermionic fields (Dirac equation, anticommutation relations, spinors), quantization of gauge fields (Abelian and non-Abelian gauge theories and covariant derivatives), interactions in quantum field theory (Feynman diagrams, scattering amplitudes, perturbation theory, and renormalization), spontaneous symmetry breaking, renormalization group, and quantum field theory in curved spacetime.
Throughout the course, students will develop a solid understanding of the mathematical and conceptual foundations of quantum field theory. They will become familiar with advanced techniques, including Feynman diagrams, loop calculations, and the renormalization group, enabling them to analyze and compute observables in realistic field theories. Successful completion of this course will equip students with the necessary tools to pursue research in high-energy physics, condensed matter physics, or other related fields.
A strong background in classical mechanics, electromagnetism, and quantum mechanics is assumed. (4 credits)
- Experimental Physics Practicum
The Experimental Physics Practicum is a graduate-level course designed to provide students with hands-on experience in conducting experiments and developing practical skills in experimental physics. This course aims to bridge the gap between theoretical concepts and their real-world applications by immersing students in the process of designing, performing, analyzing, and presenting experimental investigations.
Course Objectives
- Develop Practical Skills: Students will acquire essential laboratory skills such as setting up experimental apparatus, handling instruments, data acquisition, calibration, error analysis, and troubleshooting.
- Experimental Design: Students will learn how to formulate research questions, design experimental setups, and devise appropriate methodologies to investigate specific physical phenomena.
- Data Acquisition and Analysis: Students will gain proficiency in acquiring experimental data using advanced instruments and techniques, and learn various statistical and computational methods for analyzing and interpreting the acquired data.
- Communication and Documentation: Students will develop skills in scientific communication by preparing comprehensive experimental reports, presenting findings to peers and faculty, and engaging in critical discussions of experimental results.
Successful completion of undergraduate coursework in physics, including classical mechanics, electromagnetism, quantum mechanics, and laboratory courses. (4-8 credits)
Since the 17th century, the physical world has been viewed as “external” to consciousness. This distinction served a practical purpose when scientific theories were in their infancy and instruments rudimentary.
In our graduate physics program, you’ll gain a comprehensive understanding and mastery in both theoretical and experimental physics.
Physics today faces profound challenges. For example, how do we integrate general relativity with quantum field theory? This complex puzzle remains at the forefront of scientific exploration.
You’ll also have the unparalleled opportunity to transcend mere theory and directly experience the unified field of all the laws of nature deep within yourself.
Sunita Martin is this program’s admissions counselor for US students. Sunita will provide you with all the details of becoming a student, including connecting you with program faculty when you have questions.
