Applied Physics

This course covers a broad spectrum of mathematical techniques essential to the solution of advanced problems in physics and engineering. Topics include ordinary and partial differential equations, contour integration, tabulated integrals, saddlepoint methods, linear vector spaces, boundary-value problems, eigenvalue problems, Green’s functions, integral transforms, and special functions. Application of these topics to the solution of problems in physics and engineering is stressed. Prerequisite(s): Vector analysis and ordinary differential equations (linear algebra and complex variables recommended).

Maxwell’s equations are derived and applied to the study of topics including electrostatics, magnetostatics, propagation of electromagnetic waves in vacuum and matter, antennas, wave guides and cavities, microwave networks, electromagnetic waves in plasmas, and electric and magnetic properties of materials. Prerequisite(s): Knowledge of vector analysis, partial differential equations, Fourier analysis, and intermediate electromagnetics.

Students will receive an overview of sensors and methods to build networks and systems using sensors. The physics of detectors including fundamental technologies and sampling interfaces will be discussed. Sensor technologies for chemical, biological, nuclear, and radiological detection will be studied in detail. Evaluation methods will be presented for sensor selection based on application-specific information including sensor performance, environmental conditions, and operational impact. DODAF 2.0 methods will be taught and a project based on several viewpoints will be required and presented. Additional studies will include methods for combining results from various sensors to increase detection confidence. As part of the course, students will be given a threat scenario and will be required to select a sensor suite and networking information to design a hypothetical system considering the threat, sensor deployment cost, and logistics. Prerequisite(s): An undergraduate degree in engineering, physics, or a related technical discipline.

After a brief historical review of thermodynamics and statistical mechanics, the basic principles of statistical mechanics are presented. The classical and quantum mechanical partition functions are discussed and are subsequently used to carry out derivations of the basic thermodynamic properties of several different systems. Topics discussed include Planck’s black body radiation derivation and the Einstein-Debye theories of the specific heats of solids. The importance of these topics in the development and confirmation of quantum mechanics is also examined. Other topics discussed include Fermi Dirac and the Bose-Einstein statistics and the cosmic background radiation. The importance of comparisons between theory and data is stressed throughout.

This is an advanced course in classical mechanics that introduces techniques that are applicable to contemporary pure and applied research. The material covered provides a basis for a fundamental understanding of not only quantum and statistical mechanics but also nonlinear mechanical systems. Topics include the Lagrangian and Hamiltonian formulation of classical mechanics, Euler’s rigid body equations of motion, Hamilton-Jacobi theory, and canonical perturbation theory. These methods are applied to force-free motion of a rigid body, oscillations of systems of coupled particles, and central force motion including the Kepler problem and scattering in a Coulomb potential. Applications are emphasized through in-class examples and homework.

Prerequisite(s): Intermediate mechanics and EN.615.641 Mathematical Methods for Physics and Engineering.

This course presents the basic concepts and mathematical formalism of quantum mechanics. Topics include the mathematics of quantum mechanics, the harmonic oscillator and operator methods, quantum mechanics in three dimensions and angular momentum, quantum mechanical spin, quantum statistical mechanics, approximation methods, and quantum theory of scattering.

Prerequisite(s): Undergraduate courses in differential equations, multi-variable calculus, linear algebra, and complex variable theory or EN.615.641 Mathematical Methods for Physics and Engineering or the equivalent.AND EN.615.653 Classical Mechanics

The course is intended as an introduction to planetary science as a field of study. A basic understanding of all Solar System bodies will be provided, as well as an introduction to the missions, instruments, and tools that have been used to explore them. The vision for the designed course is to excite the students about exploration of the Solar System, and encourage them to learn more about either one particular body (ex. Mars, Venus, etc.) or one particular way of studying planets (ex. spectroscopy, mapping, etc). This course could be a direct lead in to either EN.615.663 Physics in Lunar Exploration or EN.615.664 Introduction to Exoplanets.

In this course we explore the properties of stellar interiors in order to understand stellar structure and evolution. Our emphasis will be on the fundamental physics of matter and radiation at high pressure and temperature. Topics will include star formation by gravitational collapse, thermodynamics of matter and radiation, hydrostatic equilibrium, radiative and convective heat transport, energy production in stars (burning of Hydrogen, Helium, and advanced burning), endpoints of stellar evolution (white dwarfs, neutron stars, and black holes). Familiarity with multi-variable calculus, classical mechanics, thermodynamics, statistical mechanics, and quantum mechanics at the undergraduate level is required.

Prerequisite(s): Undergraduate courses in statistical mechanics, quantum mechanics, multivariable calculus, and differential equations,Or EN.615.651 Statistical Mechanics OR EN.615.654 Quantum Mechanics.

NASA is returning to the Moon. Through lectures, discussion, and projects, this course provides a comprehensive survey of the ‘why’ and ‘how’ of lunar exploration from the distant past to the near future. Topics include the history of lunar exploration, the Moon’s orbit, analytical laboratory techniques, remote sensing techniques, in situ resource utilization, and much more. For each topic, the background and underlying physics are described and solutions discussed. References for in depth analysis are also provided. Comprehensive discussions re-enforce critical concepts each week. Students will engage in four projects over the course that will explore the Moon’s orbit, conceptualize a lunar orbiter, and produce hypothetical exploration missions placed in the 1970s and today. Students will discuss the physical consequences for errors and misconceptions of the Moon and lunar exploration in popular media. These projects will require students to engage in a range of individual and team presentation formats. Upon completion, students will be well-situated to identify companion courses in the curriculum for follow-on in depth, quantitative skills development.

This course will introduce students to the interdisciplinary study of exoplanets, a rapidly changing field leading the way to constraining the prevalence of life in our galaxy. Blending concepts from astronomy, physics, and planetary science, we will explore how planets orbiting stars elsewhere in the galaxy are discovered and characterized. We will review the latest theories in how planets form and evolve and examine trends across the exoplanet population. We will tackle the question: “Are we alone?” and compare these strange new worlds to our own Solar System. Throughout we will highlight the latest results from space missions like the James Webb Space Telescope and delve into the critical role of past, present, and future missions in solving open questions in exoplanet science.

This course covers a broad spectrum of topics related to the development of quantum and relativity theories. The understanding of modern physics and its applications is essential to the pursuit of advanced work in materials, optics, and other applied sciences. Topics include the special theory of relativity, particle-like properties of light, wave-like properties of particles, wave mechanics, atomic and nuclear phenomena, elementary particles, statistical physics, solid state, astrophysics, and general relativity.Prerequisite(s): Undergraduate degree in physics or engineering.

This course provides an integrated introduction to Earth science, emphasizing Earth as a coupled nonlinear, dynamical system composed of interacting physical, chemical, biological, and human components. Students examine Earth’s planetary evolution and the major Earth system spheres—lithosphere, hydrosphere, atmosphere, biosphere, and cryosphere—using modern Earth observations and modeling. The course incorporates foundational concepts in artificial intelligence (AI) as applied to Earth system data and modeling. Students examine how AI methods complement physically based approaches in the analysis of observations and in Earth system simulation and forecasting.

This course teaches the student the fundamental principles of geometrical optics, radiometry, vision, and imaging and spectroscopic instruments. It begins with a review of basic, Gaussian optics to prepare the student for advanced concepts. From Gaussian optics, the course leads the students through the principles of paraxial ray-trace analysis to develop a detailed understanding of the properties of an optical system. The causes and techniques for the correction of aberrations are studied. The course covers the design principles of optical Instruments, telescopes, microscopes, etc. The techniques of light measurement are covered in sessions on radiometry and photometry. Prerequisite(s): Undergraduate degree in physics or engineering.

This course covers a broad spectrum of materials-related topics designed to prepare the student for advanced study in the materials arena. Topics include atomic structure, atom and ionic behavior, defects, crystal mechanics, strength of materials, material properties, fracture mechanics and fatigue, phase diagrams and phase transformations, alloys, ceramics, polymers, and composites. Prerequisite(s): An undergraduate degree in engineering, physics, or a related technical discipline.

Why can the nuclear fuel cladding in a fission reactor cause an explosion in the core? If SiC vaporizes in a gas-turbine environment, why have SiC ceramic matrix composites become standard in aerospace engines? Why do all materials seemingly vaporize in the cold vacuum of very low earth orbit? Why is the precious metal iridium an excellent material for both jewelry and hypersonics? How can cork keep astronauts comfortable during atmospheric re-entry? This course will teach students fundamental material degradation mechanisms that drive materials selection and material failure in extreme environments, such as oxidation, creep, fatigue, embrittlement, interdiffusion, thermal cycling and coefficient of thermal expansion mismatch, stability under fission and fusion irradiation. A thorough understanding of various extreme environments will be gained and used to understand legacy and recent advanced materials selection for a variety of applications, such as industrial and aerospace gas turbines, nuclear fission and fusion reactors, very low earth orbit, hypersonics, and re-entry. Specific material systems to be covered are Ni-base superalloys, oxidation resistant overlay coatings, thermal barrier coatings, SiC ceramic matrix composites, environmental barrier coatings, accident tolerant fuel cladding, atomic oxygen resistant polymers, thermal protection systems, and ultrahigh temperature ceramics.

This course teaches the principles and techniques of quantum measurement and quantum sensing. Students will learn how quantum systems can be used to detect time, magnetic fields, and gravitational forces. Topics for this course include quantum state preparation and measurement, entanglement, and applications in atomic clocks, interferometry, and magnetometry. This course combines the foundations of quantum measurement and sensing with case studies of experimental platforms and emerging technologies.

This advanced elective course will emphasize the interaction of atoms and molecules with light, as appropriate for the modern laser era. Beginning with quasi-classical features of two-level atoms, we move on to atom-light interactions with selection rules and “forbidden transitions.” Internal structure of the atom will be treated with the theory of the Hydrogen-like atoms, including spin-orbit terms, and calculation of the fine structure and hyperfine structure using perturbation theory. Atoms in magnetic and electric fields. Beginning with helium, we will discuss multi-electron atoms, and introduce multi-electron approximation methods such as the Hartree-Fock self-consistent fields, LCAO (linear combination of atomic orbitals), and DFT (density functional theory). We will discuss vibrational and rotational spectra of simple molecules such as diatomics, and general properties of multi-atom molecules. Important time-dependent processes such as fluorescence decay, optical transitions, and collisions will be discussed. Finally, we will discuss experimentation and applications such as cesium atomic clocks, optical pumping, laser cooling and Bose-Einstein condensation. Where possible, practical examples will be chosen from atomic and molecular species of interest to atmospheric science and space science.

Prerequisite(s): 615.654 Quantum Mechanics (or equivalent) and 615.641 Mathematical Methods or similar. 615.642 Electromagnetics would be useful.

This is the first course in a two-course series (second course is 615.745) where students learn the fundamentals of designing space systems. The focus is on the underlying physics of major spacecraft subsystems, orbits, and launch vehicles. In this first course, topics include an overview of space systems engineering, the space environment, astrodynamics, space communications, orbit determination, propulsion, and spacecraft attitude determination and control. Concepts are introduced through lectures and then reinforced through homework assignments that include modeling, simulation, and analysis using MATLAB.Prerequisites: College courses in physics, calculus, and linear algebra.

This is the second course in a two-course series (first course is 615.644) that teaches a physics-based approach to space systems engineering. The focus is on the underlying physics of major spacecraft subsystems, orbits, launch vehicles, and other mission considerations. This provides a crucial foundation for informed decision making when applying systems engineering processes (requirements and risk management, verification and validation, etc.) to space systems. This second course emphasizes design through a project consisting of several interrelated homework assignments and other activities. The project is a proposal of a preliminary space mission design based on analyses established in the two-course series. Topics covered in this course include mission design, power systems, thermal control, communications, launch selection, sizing spacecraft components, and tools for design iteration. Concepts are introduced through lectures and then reinforced through homework assignments, visualization tools, modeling, simulation, analysis with MATLAB.

Prerequisite(s): EN.615.744 The Physics of Space Systems I or permission of instructors.

The primary objective of this course is to present recent advances made in the field of sensors. A broad overview includes optical, infrared, hyperspectral, terahertz, biological, magnetic, chemical, acoustic, and radiation sensors. The course will examine basic sensor operation and the implementation of sensors in measurement systems. Other topics to be covered are physical principles of sensing, interface electronic circuits, and sensor characteristics. Prerequisite(s): An undergraduate degree in engineering, physics, or a related technical discipline.

After a brief review of the theory of special relativity, the mathematical tools of tensor calculus that are necessary for understanding the theory of general relativity will be developed. Relativistic perfect fluids and their stress-energymomentum tensor will be defined, and Einstein’s field equations will be studied. Gravitational collapse will be introduced, and the Schwarzschild Black Hole solution will be discussed.

Prerequisite(s): EN.615.653 Classical Mechanics.AND either: undergraduate courses in differential equations, multi-variablecalculus, linear algebra,Or: EN.615.641 Mathematical method for physics and engineering.

This course covers the fundamental principles of modern physical optics and contemporary optical systems. Topics include propagation of light, polarization, coherence, interference, diffraction, Fourier optics, absorption, scattering, dispersion, and image quality analysis. Special emphasis is placed on the instrumentation and experimental techniques used in optical studies.

Prerequisite(s): EN.615.642 Electromagnetics or the equivalent completed or taken concurrently.

This course is an introduction to the physical processes that govern the “fourth state of matter”, also known as plasma. Plasma physics is the study of ionized gas, which is the state of the matter for 99.9% of the apparent universe, from astrophysical plasmas, to the solar wind and Earth’s radiation belts and ionosphere. Plasma phenomena are also relevant to energy generation by controlled thermonuclear fusion. The challenge of plasma physics comes from the fact that many plasma properties result from the long-range Coulomb interaction, and therefore are collective properties that involve many particles simultaneously. Topics to be covered during class include motion of charged particles in electric and magnetic fields, dynamics of fully ionized plasma from both microscopic and macroscopic points of view, magneto-hydrodynamics, equilibria, waves, instabilities, applications to fusion devices, ionospheric, and space physics. .

Prerequisite(s): EN.615.642 Electromagnetics or the equivalent

This course studies the physics and the history of our utilization of space, the challenges and mitigation of making in situ observations in space. Topics include the history of solar system exploration; the solar cycle; the electrodynamics of the solar upper atmosphere responsible for the solar wind; and the solar wind interaction with unmagnetized and magnetized bodies—how this leads to planetary bow shocks, comets, and magnetospheres and how they are studied. Practical issues include penetrating radiation and its effects on spacecraft and man in space, magnetospheric storm disruptions of ground power distribution and spacecraft charging in the presence and absence of solar illumination with particular reference to applying this knowledge in exploring the outer solar system and beyond.

Prerequisite(s): EN.615.642 Electromagnetics or the equivalent.

Students examine concepts and methods employed in condensed matter physics with applications in materials science, surface physics, and electronic devices. Topics include atomic and electronic structure of crystalline solids and their role in determining the elastic, transport, and magnetic properties of metals, semiconductors, and insulators. The effects of structural and chemical disorder on these properties are also discussed.

Prerequisite(s): EN.615.654 Quantum Mechanics or the equivalent.

This course examines the physical principles underlying semiconductor device operation and the application of these principles to specific devices. Emphasis is placed on understanding device operation, rather than on circuit properties. Topics include elementary excitations in semiconductors such as phonons, photons, conduction electrons, and holes; charge and heat transport; carrier trapping and recombination; the pn junction; transistors; photodetectors; LEDs; and solar cells. Prerequisite(s): An undergraduate degree in engineering, physics, or a related technical discipline. An undergraduate level familiarity with quantum mechanics would be helpful.

This course covers the physical concepts and mathematics of the exciting field of oceanography and can be taken as an elective. It is designed for the student who wants to learn more about oceanography. Topics range from fundamental small waves to planetary-scale ocean currents. There will be a strong emphasis on understanding the basic ocean processes. Initial development gives a description of how the ocean system works and the basic governing equations. Additional subjects include boundary layers, flow around objects (seamounts), waves, tides, Ekman flow, and the Gulf Stream. Also studied will be the ocean processes that impact our climate such as El Nino and the Thermohaline Conveyor Belt. Prerequisite(s): Mathematics through calculus.

This course introduces the numerical methods and computer tools required for the practical applications of the electromagnetic concepts covered in EN.615.642 to daily-life engineering problems. It covers the methods of calculating electromagnetic scattering from complex air and sea targets (aircraft, missiles, ships, etc.), taking into account the effects of the intervening atmosphere and natural surfaces such as the sea surface and terrain. These methods have direct applications in the areas of radar imaging, communications, and remote sensing. Methods for modeling and calculating long-distance propagation over terrain and in urban areas, which find application in the areas of radar imaging, radio and TV broadcasting, and cellular communications, are also discussed. The numerical toolkit built in this course includes the method of moments, the finite difference frequency and time domain methods, the finite element method, marching numerical methods, iterative methods, and the shooting and bouncing ray method. Prerequisite(s): Knowledge of vector analysis, partial differential equations, Fourier analysis, basic electromagnetics, and a scientific computer language.

In this course the physics behind the operation of modern infrared (IR) detectors and sensors systems will be elucidated. This will include not only the physics and technology behind the detectors themselves but also the associated technologies such as optics, coolers and readout integrated circuits (ROICs). The course will begin with a history of the development of IR detectors. Next basic concepts needed to describe the performance of the detectors and sensor systems will be described and finally there will be examples of applications to modern IR sensor systems used in the ground, airborne and space domains.

The course will introduce students to the basic concepts of nonlinear physics, dynamical system theory, and chaos. These concepts will be studied by examining the behavior of fundamental model systems that are modeled by ordinary differential equations and, sometimes, discrete maps. Examples will be drawn from physics, chemistry, and engineering. Some mathematical theory is necessary to develop the material. Practice through concrete examples will help to develop the geometric intuition necessary for work on nonlinear systems. Students conduct numerical experiments using provided software, which allows for interactive learning. Prerequisite(s): Mathematics through ordinary differential equations. Familiarity with MATLAB is helpful. Consult instructor for more information.

This course exposes the student to the physical principles underlying satellite observations of Earth by optical, infrared, and microwave sensors, as well as techniques for extracting geophysical information from remote sensor observations. Topics will include spacecraft orbit considerations, fundamental concepts of radiometry, electromagnetic wave interactions with land and ocean surfaces and Earth’s atmosphere, radiative transfer and atmospheric effects, and overviews of some important satellite sensors and observations. Examples from selected sensors will be used to illustrate the information extraction process and applications of the data for environmental monitoring, oceanography, meteorology, and climate studies.

This course begins with a brief review of tensor calculus and principles of the General theory of relativity, the Freidmann equation and the Robertson-Walker metric. Cosmological models including radiation, matter, and the cosmological constant and their properties are discussed. Observational parameters, the role of dark matter, and the cosmic microwave background, and nucleosynthesis in the early universe are studied. The flatness and the horizon problems are introduced and the role of inflation in the early universe is discussed. Finally, we discuss the origins and the role of density fluctuations in formation of large structures leading to the current Cosmological constant Cold Dark Matter model of the universe.

Prerequisite(s): EN.615.748 Introduction to Relativity.

To understand the forces that cause global climate variability, we must understand the natural forces that drive our weather and our oceans. This course covers the fundamental science underlying the nature of the Earth’s atmosphere and its ocean. This includes development of the basic equations for the atmosphere and ocean, the global radiation balance, description of oceanic and atmospheric processes, and their interactions and variability. Also included will be a description of observational systems used for climate studies and monitoring, fundamentals underlying global circulation, and climate prediction models. Prerequisite(s): Undergraduate degree in physics or engineering or equivalent, with strong background in mathematics through the calculus level.

This course will dive into NISQ algorithms and their implementation on currently available quantum processors. It will begin with an overview of quantum circuits and the IBM Qiskit API, a popular tool for constructing, simulating, and experimentally executing quantum circuits. After briefly discussing the current limitations of NISQ devices, we will begin exploring NISQ era quantum algorithms. First, we will discuss variational quantum algorithms, a hybrid quantum-classical approach ubiquitously used in modern quantum computing. We will cover applications for solving classical optimization problems on quantum hardware and finding ground states of molecular systems. Finally, we will focus on the use of quantum processors for the simulation of time dynamics of quantum systems.

In this course, students learn to design optical systems and model their performance. Students will use commercially available optical design software to complete their assignments and their design project. We will begin with simple lenses for familiarization with optical design software using CODE V, and then move onto more complicated multi-element lenses and reflective systems. For their design project, students may use any software of their choosing (e.g. OSLO, ZEMAX, OpTalix, SYNOPSYS, their own, etc.). Emphasis is placed on understanding the optical concepts involved in the designs while developing the ability to use design software to properly model optical systems. Upon completion of the course, students are capable of independently pursuing their own optical designs and building optical models of existing systems.

Prerequisite(s): EN.615.671 Principles of Optics

This course examines the physics of detection of incoherent electromagnetic radiation from the infrared to the soft X-ray regions. Brief descriptions of the fundamental mechanisms of device operation are given. A variety of illumination sources are considered to clarify detection requirements, with emphasis on solar illumination in the visible and blackbody emission in the infrared. Practical devices, elementary detection circuits, and practical operational constraints are described. An introduction to solid-state and semiconductor physics follows and is then applied to the photodiode, and later to CCD and CMOS devices. A description and analysis of the electronics associated with photodiodes and their associated noise is given. Description of scanning formats leads into the description of spatially resolving systems (e.g., staring arrays). Emphasis is placed on Charged-Coupled Device and CMOS detector arrays. This naturally leads into the discussion of more complex IR detectors and Readout Integrated Circuits that are based on the CMOS pixel. In addition, descriptions of non-spatially resolving detectors based on photoemission and photo-excitation are provided, including background physics, noise, and sensitivity. Selection of optimum detectors and integration into complete system designs are discussed. Applications in space-based and terrestrial remote sensing are discussed, from simple radiometry and imaging to spectrometry. Prerequisite(s): Undergraduate degree in physics or engineering, preferably with studies in elementary circuit theory, solid-state physics, and optics. Students are expected to be proficient using spreadsheets and/or a programming language such as MATLAB or IDL.

This course provides an introduction to the rapidly developing field of quantum information processing. In addition to covering fundamental concepts such as two-state systems, measurements uncertainty, quantum entanglement, and nonlocality, the course will emphasize specific quantum information protocols. Several applications of this technology will be explored, including cryptography, teleportation, dense coding, computing, and error correction. The quantum mechanics of polarized light will be used to provide a physical context to the discussion. Current research on implementations of these ideas will also be discussed.

Prerequisite(s): EN.615.654 Quantum Mechanics

This course provides hands-on experience with MATLAB by performing weekly computer exercises revolving around optics. Each module explores a new topic in optics, while simultaneously providing experience in MATLAB. The goal is to bridge the gap between theoretical concepts and real-world applications. Topics include an introduction to MATLAB, review of electromagnetism, ray tracing, 1D Fourier theory and propagation in optical fibers, laser beam propagation, paraxial wave propagation in turbulent media, diffraction and holography, polarization and interferometry, optical waveguides and laser theory and related technologies. Students are expected to complete a semester project that will facilitate investigation of a topic of interest not specifically covered in the course. Course Note(s): No prior experience with MATLAB is required. While a background in optics is helpful, it is not required.

This course will cover the basics of superconductivity and its applications in quantum computing. We will discuss the physics of Josephson junctions and how they are used to build quantum bits (qubits). We will then study two currently popular superconducting qubits: the transmon and the fluxonium. We will also look at superconducting amplifiers, including Travelling Wave Parametric Amplifiers (TWPAs). Lastly, we will explore how these devices, including magnetometers, may be used for quantum sensing.

This course introduces open quantum systems—quantum systems that interact with their environment, leading to decoherence and entanglement loss. The course covers the main equations governing non-unitary dynamics, with emphasis on the Lindblad master equation, and explores how different noise environments are modeled in experimental settings. Students will learn key formalisms such as density matrices, quantum operations, and measurement theory, In addition, students will dive into the relevant cQED framework, which forms the basis of control and measurement in state-of-the-art architectures such as superconducting qubits.

This course is an individually tailored, supervised project that offers the student research experience through work on a special problem related to his or her field of interest. The research problem can be addressed experimentally or analytically, and a written report is produced. It is recommended that all required Applied Physics courses be completed. Open only to candidates in the Master of Science in Applied Physics program. Prerequisite(s): It is recommended that all required Applied Physics courses be completed. The Independent Study/Project proposal form (https://ep.jhu.edu/current-students/student-forms/) must be approved prior to registration. Course Note(s): Open only to candidates in the Master of Science in Applied Physics program.

In this course, qualified students are permitted to investigate possible research fields or to pursue problems of interest through reading or non-laboratory study under the direction of faculty members. Open only to candidates in the Master of Science in Applied Physics program. Prerequisite(s): The Independent Study/Project proposal form (https://ep.jhu.edu/current-students/student-forms/) must be completed and approved prior to registration. Course Note(s): Open only to candidates in the Master of Science in Applied Physics program.