Physics is all around us! If you're curious about how the world works, you will find majoring in physics quite rewarding. In addition to learning the theoretical basics that help you understand and describe physical phenomena, you will become fluent in the programming language Python and receive training in our hands-on and open-ended research projects, giving you the tools you need to become an independent and thoughtful scientist or engineer. While earning your Bachelor's degree, you will learn how to solve difficult problems well - a skill that opens doors to a wide variety of scientific and other careers. Many of our graduates pursue Master's or PhD degrees in field including physics, engineering, mathematics, education, data science, and patent law, while others transition into the workforce right away.

The physics department is located in Collins Hall. Beginning typically as early as your sophomore year, you are encouraged to join one of our ongoing research projects in astronomy, atomic/molecular physics, biophysics, cosmology, nonlinear dynamics, and optics. Individual faculty research spaces are housed in the basement of Collins, and all laboratories are equipped with a wide variety of state-of-the-art instrumentation. For more information, please visit the physics faculty page.

## Requirements for the BA in Physics (57 semester hours)

39-45 semester hours in Physics, 8 semester hours in Mathematics, 4 semester hours in Computer Science, up to 9 semester hours in allied disciplines

#### Core courses

- PHYS 221 Introductory Physics I (4)
- PHYS 221Y Introductory Physics I Lab (1)
- PHYS 222 Introductory Physics II (4)
- PHYS 222Y Introductory Physics II Lab (1)
- PHYS 223 Modern Physics (4)
- PHYS 223Y Modern Physics Lab (1)
- PHYS 390W Scientific Communication in Physics (2)
- PHYS 392 Advanced Techniques in Experimental Physics (2)
- One course chosen in from among the following:

### Choose three courses from the following (12 semester hours)

- PHYS 310 Mechanics (4)
- PHYS 320 Thermal Physics (4)
- PHYS 324 Electromagnetism (4)
- PHYS 328 Quantum Mechanics (4)

### Senior Projects

- PHYS 495W Research Seminar I (2)
- PHYS 495Y Research Seminar I Lab (2)
- PHYS 496W Research Seminar II (2)
- PHYS 496Y Research Seminar II Lab (2)

### Additional requirements

- MATH 249 Multivariable Calculus (4)
- MATH 256 Differential Equations (4)
- CS 151 Introduction to Programming with Python (4)
- Four credits at the 200 level or above chosen from any of the following disciplines: Physics, Biology, Chemistry, Environmental Science, Exercise and Health Science, Computer Science or Data Science (4)

## Requirements for the BS in Physics (57 semester hours)

45 semester hours in Physics, 8 semester hours in Mathematics, 4 semester hours in Computer Science

### Core courses

- PHYS 221 Introductory Physics I (1)
- PHYS 221Y Introductory Physics I Lab (1)
- PHYS 222 Introductory Physics II (4)
- PHYS 222Y Introductory Physics II Lab (1)
- PHYS 223 Modern Physics (4)
- PHYS 223Y Modern Physics Lab (1)
- PHYS 310 Mechanics (4)
- PHYS 320 Thermal Physics (4)
- PHYS 324 Electromagnetism (4)
- PHYS 328 Quantum Mechanics (4)
- PHYS 390W Scientific Communication in Physics (2)
- PHYS 392 Advanced Techniques in Experimental Physics (2)
- One course chosen from between the following:

### Senior Projects

- PHYS 495W Research Seminar I (2)
- PHYS 495Y Research Seminar I Lab (2)
- PHYS 496W Research Seminar II (2)
- PHYS 496Y Research Seminar II Lab (2)

### Additional requirements

- Four additional semester hours in Physics numbered above 200 (4)
- MATH 249 Multivariable Calculus (4)
- MATH 256 Differential Equations (4)
- CS 151 Introduction to Programming with Python (4)

Graduate schools often require students take courses similar to PHYS 320 (Thermal Physics), PHYS 324 (Electromagnetism), and PHYS 328 (Quantum Mechanics). Students intending to do graduate study in Physics should consider further mathematical study in linear algebra and complex variables. Students preparing for careers in engineering or applied science should consider taking PHYS 399 (Materials Science) and PHYS 324 Electromagnetism plus one other course beyond the basic six. Students with other goals in mind should consult the faculty concerning their choice of elective courses beyond the basic six.

## Requirements for the Physics Minor (23 semester hours)

- PHYS 221 Introductory Physics I (4)
- PHYS 221Y Introductory Physics I Lab (1)
- PHYS 222 Introductory Physics II (4)
- PHYS 222Y Introductory Physics II Lab (1)
- PHYS 223 Modern Physics (4)
- PHYS 223Y Modern Physics Lab (1)
- Eight additional Physics semester hours at 300- or 400-level (8)

## Indicators of Achievement

The department seeks to meet its program mission through a curriculum that emphasizes the four skill sets.## Student Learning Outcomes for the Physics Major

**Content Knowledge****:**Students have a broad theoretical physics foundation, as well as applied mathematical and computational skills, to allow them to understand, describe, and model the natural world using conceptual, mathematical, and computational approaches.**Research Skills****:**Students are able to collect data using basic and advanced lab equipment, to design and implement a year-long research project, and to properly analyze and summarize large amounts of data.**Communication Skills****:**Students know how to effectively communicate physics knowledge in a variety of formats (including via written, visual, and oral presentation), and are able to use their communication skills to work collaboratively to solve complex problems.

## Faculty

**Rick Watkins**, Professor of Physics; Department Chair**David Altman**, Professor of Physics**Daniel Borrero Echeverry**, Associate Professor of Physics**Michaela Kleinert**, Professor of Physics**Rachel Dewey-Thorsett**, Affiliated Scholar

## Visiting Professors

**Mike Vignal**, Visiting Assistant Professor of Physics

## Course Listings

### PHYS 110 Astronomy (4)

An introduction to modern theories of the universe and its evolution. Topics include naked eye observation, the solar system, stars, galaxies, and cosmology. Emphasis will be placed on the scientific method and how we understand the universe in terms of basic physical principles.

**General Education Requirement Fulfillment:**Natural Sciences**Offering:**Every Spring semester (occasionally in Fall semester)**Instructor:**Rembold, Watkins

### PHYS 199 Topics in Physics (1-4)

A semester-long study of topics in Physics. Topics and emphases will vary according to the instructor. This course may be repeated for credit with different topics. See the New and Topics Courses page on the Registrar’s webpage for descriptions and applicability to majors/minors in other departments.

**General Education Requirement Fulfillment:**Topic dependent**Prerequisite:**Topic dependent**Offering:**Occasionally**Professor:**Staff

### PHYS 221 Introductory Physics I (4)

An introduction to classical mechanics and thermodynamics. In this course students study the concepts and techniques required to measure, describe and predict the motion of particles and extended objects. Topics include kinematics of linear motion, forces and Newton's laws, gravitation, momentum, work, energy, rotational motion, angular momentum, torque, oscillations, temperature, heat, and thermal energy. A laboratory (PHYS 221Y) is associated with this course.

**General Education Requirement Fulfillment:**Natural Sciences**Prerequisite:**MATH 140 or MATH 150 or MATH 151/152 or MATH 152/153 or MATH 249 (or concurrent enrollment)**Offering:**Every semester**Instructor:**Altman, Borrero, Kleinert, Rembold, Watkins

### PHYS 222 Introductory Physics II (4)

An introduction to electricity, magnetism, and optics. In this course students study the concepts and techniques required to understand interactions between charged particles as well as light as an electromagnetic wave. Topics include electric force, electric field, electric potential, capacitance, electric current, circuits, magnetic field, inductance, Faraday's law, electromagnetic waves, sound waves, reflection, refraction, interference, diffraction and polarization. A laboratory (PHYS 222Y) is associated with this course.

**General Education Requirement Fulfillment:**Natural Sciences**Prerequisite:**PHYS 221 and MATH 140 or MATH 152/153 or MATH 249 (or concurrent enrollment in MATH courses)**Offering:**Every spring**Instructor:**Altman, Borrero, Kleinert, Rembold, Watkins

### PHYS 223 Modern Physics (4)

A survey of the major developments in physics of the 20th century, as well as an introduction to more sophisticated mathematical and laboratory techniques. Topics include special relativity, the quantum nature of light, the wave nature of particles, the Schrödinger equation, atomic physics, molecules, statistical physics, solid state physics, nuclear physics, particle physics and cosmology. A laboratory (PHYS 223Y) is associated with this course.

**General Education Requirement Fulfillment:**Natural Sciences**Prerequisite:**PHYS 222 and MATH 152**Offering:**Every fall**Instructor:**Kleinert, Watkins

### PHYS 250 Cell Biophysics (4)

This course explores how the insights of physics and mathematics have illuminated the complex phenomena of the cell. Students study the use of the quantitative and predictive models to describe biological systems, and discuss the experimental methods that provide the quantitative data required to create and test these methods. The course is structured around a series of case studies involving some of the key players in molecular and cell biology.

**General Education Requirement Fulfillment:**Natural Sciences**Prerequisite:**Complete or co-enrollment in MATH 140 or MATH 150 or MATH 151/152 or MATH 152/153 or MATH 249**Offering:**Alternate springs**Instructor:**Altman

### PHYS 299 Topics in Physics (1-4)

A semester-long study of topics in Physics. Topics and emphases will vary according to the instructor. This course may be repeated for credit with different topics. See the New and Topics Courses page on the Registrar’s webpage for descriptions and applicability to majors/minors in other departments.

**General Education Requirement Fulfillment:**Topic dependent**Prerequisite:**Topic dependent**Offering:**Occasionally**Professor:**Staff

### PHYS 310 Mechanics (4)

A study of classical mechanics developed by Newton and reformulated by Lagrange and Hamilton. Topics include vector kinematics and dynamics in Cartesian, cylindrical, and spherical form, the two-body problem, oscillations, Lagrangian mechanics, non-inertial reference frames, coupled oscillation, and rigid body motion.

**General Education Requirement Fulfillment:**Natural Sciences**Prerequisite:**PHYS 222 and MATH 249**Offering:**Fall semester**Instructor:**Staff

### PHYS 320 Thermal Physics (4)

A study of systems with a large number of particles through the methods of thermodynamics and statistical mechanics. Topics include the laws of thermodynamics, temperature, heat, thermal equilibrium, equipartition theorem, ideal gas, simple two state systems, entropy, heat engines, free energies, phase transformations, kinetic theory, partition functions, quantum statistics, degenerate Fermi gases, Bose-Einstein condensates, and blackbody radiation.

**General Education Requirement Fulfillment:**Natural Sciences**Prerequisite:**PHYS 223 and MATH 152**Offering:**Alternate falls**Instructor:**Borrero

### PHYS 324 Electromagnetism (1)

A study of electromagnetism using vector calculus. Topics include static electric and magnetic fields in vacuum and matter, electrodynamics, Maxwell's equations, and electromagnetic waves. Mathematical techniques using vector calculus, and other techniques such as solving boundary value partial differential equations will be discussed.

**General Education Requirement Fulfillment:**Natural Sciences**Prerequisite:**PHYS 222 and MATH 249**Offering:**Alternate falls**Instructor:**Borrero

### PHYS 328 Quantum Mechanics (4)

A mathematical development of quantum theory. The first part of the course focuses on solving the Schrodinger equation in one, two and three dimensions. Further topics include the theory of angular momentum, the hydrogen atom, identical particles and quantum statistics, and time-independent perturbation theory.

**General Education Requirement Fulfillment:**Natural Sciences**Prerequisite:**PHYS 223 and MATH 249**Offering:**Alternate springs**Instructor:**Watkins

### PHYS 332 Structure and Properties of Materials and Devices I (4)

This course is the first in a 3-course sequence on Materials Science and introduces students to the basics—the structure of materials. Students will learn how the underlying structure of a material determines its properties, its potential applications, and its performance within those applications. In particular, they will learn about the differences between amorphous materials (glasses, polymers) and crystals (ideal crystals, crystals with defects, liquid crystals).

This course is taught in a flipped-classroom format. Instead of using a standard textbook, students will watch online lectures provided by Massachusetts Institute of Technology before coming to class. Class time will be used to solidify the material through in-class discussions and practice problems. This class meets jointly with Structure and Properties of Materials and Devices II and III.

**General Education Requirement Fulfillment:**Natural Sciences**Prerequisite:**PHYS 223 and MATH 152 or higher**Offering:**Spring semester**Instructor:**Kleinert, Altman

### PHYS 333 Structure and Properties of Materials and Devices II (1-4)

This course is the second in a 3-course sequence on Materials Science and introduces students to the underlying quantum mechanical and electromagnetic description of materials. These powerful physical theories are used to understand and describe the origins of the electronic, optical, and magnetic properties of materials. Students will also see basic applications such as diodes, optical fibers, LEDs, and solar cells.

This course is taught in a flipped-classroom format. Instead of using a standard textbook, students will watch online lectures provided by the Massachusetts Institute of Technology before coming to class. Class time will be used to solidify the material through in-class discussions and practice problems. This class meets jointly with Structure and Properties of Materials and Devices I and III.

**General Education Requirement Fulfillment:**Natural Sciences**Prerequisite:**PHYS 223**Offering:**Spring semester**Instructor:**Kleinert, Altman

### PHYS 334 Structure and Properties of Materials and Devices III (4)

In this course, students will learn how everyday devices can be designed to take advantage of the electrical, optical, and magnetic properties that were investigated in the second course of this 3-course sequence. Applications include diodes, transistors, photodetectors, solar cells, displays, LEDs, lasers, optical fibers, photonic devices, magnetic data storage, motors, transformers, and spintronics.

This course is taught in a flipped-classroom format. Instead of using a standard textbook, students will watch online lectures provided by the Massachusetts Institute of Technology before coming to class. Class time will be used to solidify the material through in-class discussions and practice problems. This class meets jointly with Structure and Properties of Materials and Devices I and II.

**General Education Requirement Fulfillment:**Natural Sciences**Prerequisite:**PHYS 223 and MATH 152 or higher and PHYS 333**Offering:**Spring semester**Instructor:**Kleinert, Altman

### PHYS 340 Advanced Data Analysis and Simulation (ADAS) (2)

This course focuses on advanced data analysis methods used for conducting research in physics. Coursework will consist of worksheets, where students learn concepts by carrying out computational exercises and simulations in the python programming language, alternating with projects where students analyze real data and communicate their results in written reports. Topics covered may include error distributions, Bayesian parameter estimation, Markov Chains, Monte Carlo techniques, and machine learning

**General Education Requirement Fulfillment:**Natural Sciences**Prerequisite:**PHYS 222**Offering:**Fall**Instructor:**Watkins

### PHYS 342 General Relativity and Cosmology (4)

This course introduces advanced Physics and Math majors to the fields of general relativity and cosmology. Students will develop an understanding of gravity as an outcome of curved spacetime. Topics covered will include: black holes, gravitational waves, and the structure and evolution of the Universe.

**General Education Requirement Fulfillment:**Natural Sciences**Prerequisite:**MATH 249**Offering:**Alternate Fall semesters**Instructor:**Watkins

### PHYS 344 Fundamentals of Optics (2)

In this course, students study geometrical optics (ray optics, reflection, refraction, and matrix optics), wave optics (the complex wave function, the paraxial wave equation and its solutions, lasers, interference, holography), and Gaussian optics (Gaussian laser beams and the complex q-parameter). Basic knowledge of how to work with matrices is encouraged but not required.

**General Education Requirement Fulfillment:**Natural Sciences**Prerequisite:**PHYS 223, MATH 249, MATH 253 or basic knowledge of matrices recommended.**Offering:**Alternate Fall semesters**Instructor:**Kleinert

### PHYS 346 Nonlinear Dynamics and Chaos (4)

This course engages the student in the qualitative analysis of nonlinear dynamical equations, including their features (e.g., the existence and stability of fixed points and limit cycles, dynamical bifurcations, and chaotic behavior), as well as the study of nonlinear maps and fractals. Mathematical and computational concepts will be gradually introduced and emphasis will be given to specific examples drawn from a range of natural sciences, social sciences, and engineering, which facilitate the understanding of dynamical systems theory and emphasize its relevance in practical applications. Supplementary topics include the study of pattern forming systems, the emergence of spatiotemporal complexity in high-dimensional systems, and spontaneous self-organization.

**General Education Requirement Fulfillment:**Natural Sciences**Prerequisite:**MATH 249**Offering:**Alternate Spring semesters**Instructor:**Borrero

### PHYS 354 Advanced Topics in Optics (2)

In this course, students study advanced topics in optics. Topics may vary, but typically include Fourier optics, polarization, and the basics of quantum optics/quantum information, and will typically be centered around two important experiments. Basic knowledge of how to work with matrices is encouraged but not required.

**General Education Requirement Fulfillment:**Natural Sciences**Prerequisite:**PHYS 223, MATH 249. MATH 253 or basic knowledge of recommended. Taking PHYS 344 prior to this course is encouraged but not required.**Offering:**Alternate Spring semesters**Instructor:**Kleinert

### PHYS 360 Research Experience in Physics (1-2)

Research experience in ongoing state-of-the-art research projects in the physics department. Sophomores and juniors can sign up for this 1-semester hour course. Work requirement is about 3 hours/week. May be repeated up to four times for credit before the senior year.

**General Education Requirement Fulfillment:**Natural Sciences**Prerequisite:**Instructor consent**Offering:**Every semester**Instructor:**Altman, Borrero, Kleinert

### PHYS 390W Scientific Communication in Physics (2)

In this course students will develop skills related to finding, reading, and understanding physics literature and communicating physics concepts in writing, as a poster, and orally. Students will also develop and write their senior research proposal and present it at the end of the class.

**General Education Requirement Fulfillment:**Writing-centered; Natural Sciences**Prerequisite:**PHYS 223**Offering:**Every semester**Instructor:**Altman, Borrero, Kleinert

### PHYS 392W Advanced Techniques in Experimental Physics (2)

In this course, students gain hands-on experimental research skills by carrying out independent projects. Topics for the course vary, and will be selected by the instructor.

**General Education Requirement Fulfillment:**Natural Sciences**Offering:**Spring**Instructor:**Altman, Borrero, Kleinert

### PHYS 399 Topics in Physics (1-4)

A semester-long study of topics in Physics. Topics and emphases will vary according to the instructor. This course may be repeated for credit with different topics. See the New and Topics Courses page on the Registrar’s webpage for descriptions and applicability to majors/minors in other departments.

**General Education Requirement Fulfillment:**Topic dependent**Prerequisite:**Topic dependent**Offering:**Occasionally**Professor:**Staff

### PHYS 429 Topics in Physics (1-4)

**General Education Requirement Fulfillment:**Topic dependent**Prerequisite:**Topic dependent**Offering:**Occasionally**Professor:**Staff

### PHYS 490 Independent Study (1 or 2 or 4)

Individual programs of independent study of topics selected in consultation with faculty. This includes, but is not limited to, additional course work or independent research projects.

**General Education Requirement Fulfillment:**Natural Sciences**Offering:**Every semester**Instructor:**Staff

### PHYS 495W Research Seminar I (2)

Required Senior Year Experience for all resident Physics majors. In the accompanying lab course, students design and carry out individual research projects under the mentorship of a departmental faculty member. During weekly meetings, students attend seminar talks, discuss research methods, engage in peer mentoring, and practice scientific communication skills. A significant amount of class time will be spent writing and peer-reviewing senior theses. The course culminates in a progress report that is given as a formal oral presentation.

**General Education Requirement Fulfillment:**Natural Sciences**Corequisite:**PHYS 495YW**Offering:**Every fall**Instructor:**Altman, Borrero, Kleinert, Rembold, Watkins

### PHYS 496W Research Seminar II (2)

Required Senior Year Experience for all resident Physics majors. In the accompanying lab course, students continue individual research projects under the mentorship of a departmental faculty member. During weekly meetings, students attend seminar talks, discuss research methods, engage in peer mentoring, and practice scientific communication skills. A significant amount of class time will be spent writing and peer-reviewing senior theses. The course culminates in a written senior thesis and a formal oral presentation during Willamette's annual Student Scholarship Recognition Day (SSRD)

**General Education Requirement Fulfillment:**Natural Sciences**Corequisite:**PHYS 496YW**Offering:**Spring**Instructor:**Altman, Borrero, Kleinert, Rembold, Watkins