### Learning Outcomes

Upon graduation from Dickinson, Physics majors will be able to:

- design and perform scientific experiments in physics and evaluate the data in graphical form;
- describe significant concepts and theories in the fundamental areas of physics (mechanics, thermodynamics, electromagnetism, relativity, and quantum mechanics);
- analyze, interpret, and communicate results from advanced physics topics in written form.

### Major

A physics major consists of a minimum of 11 courses, usually five core courses, at least four electives, and two courses of research during the senior year. Students should be aware that most physics courses have mathematics corequisites and/or prerequisites, as listed in the course description. Courses above the 200-level typically require a facility with multivariate calculus (normally requiring completion of two courses in mathematics). Each student majoring in physics is expected to acquire a basic knowledge of classical and modern physics by taking a core sequence consisting of two semesters of workshop physics (131, 132 or 141, 142) followed by 211, 212 and 282. Students will then select at least four elective courses tailored to their preparation, interests, and goals. At least two of these must be at the 300-level or above. All physics majors not enrolled in a 3-2 engineering program must complete the Advanced Laboratory Capstone sequence 491, 492 *OR *two semesters of Independent Research (PHYS 550) with senior status and permission of the instructor. The introductory courses intended primarily for non-science majors, Life in the Universe (ASTR 105), Mysteries of the Solar System (ASTR 109), and Stars, Galaxies, and Beyond! (ASTR 110) may not be applied towards a physics major.

**Physics-Engineering Track**

13 courses

PHYS 131, 132, 211, 212, 213, 282, 311, 312, 331 OR 314, 491 and 492

COMP 130

CHEM 131 OR 141

### Minor

**Minor in Physics**

A physics minor is expected to acquire a basic knowledge of classical and modern physics by taking six of the department's course offerings, including a two semester workshop physics sequence (131, 132 or 141, 142) and 212. The remaining three courses required for the minor must be at or above the 200-level. A student may not apply courses used to fulfill the requirements of a minor in physics to fulfill the requirements of a minor in astronomy.

**Minor in Astronomy**

Options are available for students who wish to add an astronomical perspective to a major in any field. The minor consists of the following: ASTR 109, PHYS 131, PHYS 132, ASTR/PHYS 208, PHYS 212, and ASTR/PHYS 306 *OR* one other astronomy-related course offered in the Physics and Astronomy Department, which may include an independent study, independent research, or internship credit offered by the Department of Physics and Astronomy. One of these courses/experiences may, upon prior approval by the Department, be offered by another department or be an external experience such as a summer Research Experience for Undergraduates. No more than three of these courses or experiences may count toward both the physics major and the astronomy minor. *Note that there are mathematics prerequisites for PHYS 131, 132 and 212.*

### Suggested curricular flow through the major

**Physics Major**

The Physics major is designed to allow students to start in either the first year or the sophomore year.

The following are suggested courses for a student starting the first year:

*First Year*

PHYS 131/132

MATH 151/170 or 170/171

*Sophomore Year*

PHYS 211, 212, 282

MATH 270 or 171/270

*Junior Year*

Four 300-level or above Physics courses, including 311, 331 or 431 (depending on course offerings)

PHYS 392 (half-credit junior seminar)

*Senior Year*

PHYS 491, 492 OR two semesters of Independent Research 550 (usually with a common theme); 312, 331 or 431

**First-years**: Students should be advised to take PHYS 131/132 and MATH 151/170 or 170/171

**Physics-Engineering Track**

*First year*

PHYS 131/132

MATH 170/171

*Sophomore Year*

PHYS 211, 212, 282

MATH 270

CHEM 131 or 141

*Sophomore or Junior Year *

PHYS 213

*Junior Year*

PHYS 311, PHYS 331 or PHYS 314

COMP 130

*Senior Year*

PHYS 312, 491, 492

Students planning to do graduate study in physics, astronomy or engineering need to include 311 and 312 (potentially 331 and/or 431 as well, depending on field of study). For students not planning to do graduate study in physics or engineering, options include 313, 314, 315 and 361 as offered. Students planning to do graduate study in astronomy need to additionally take 208, 306 or 406 as offered.

**Astronomy Minor**

*First Year*

PHYS 131/132

ASTR 109

*Sophomore Year*

ASTR/PHYS 208

PHYS 212

*Junior Year*

ASTR/PHYS 306

*Senior Year*

1 additional course

**First-years**: Students should be advised to take PHYS 131, PHYS 132, and ASTR 109

### Independent study and independent research

Independent study or research is strongly encouraged by the department. Independent research projects are readily available in the many areas, including pattern formation, solar air heaters, non-linear dynamics, molecular and laser physics, and astrophysics. Independent research students have often published papers and/or given talks at physics and astronomy meetings. Students planning on graduate study are encouraged to discuss with faculty the independent research opportunities available.

### Honors

Students in the Advanced Capstone Laboratory (PHYS 491/492) or students participating in two semesters of Independent Research (PHYS 550) may choose to turn their project into an honors project with an in-depth paper and an oral defense before the physics faculty. For more detailed requirements, go to the department's web site.

### Courses

**Courses in Astronomy**

105 Life in the Universe

A comprehensive study of the astronomical possibilities of extraterrestrial life including a brief survey of the universe, conditions necessary for life, and astronomical observations (including UFOs) which support or deny the premise that life in the universe is a common phenomenon.

109 Mysteries of the Solar System

This course explores questions that are as old as humanity; you will step into the shoes of ancient astronomers to ponder the workings of the night sky and Solar System. Why do the stars move the way they do? Why do some bright objects wander the night sky? Can we know what these objects are and where they came from? We will develop practical and critical thinking skills that are crucial to the art of discovery, focusing on the historical use of naked eye and telescopic observations, as well as the use of present day space probes and the electromagnetic spectrum. Our journey will take us to the planets and some fascinating moons. *Three hours classroom, one two-hour laboratory a week. This course counts toward the astronomy minor.*

Attributes: Appropriate for First-Year, Lab Sciences, Quantitative Reasoning

110 Stars, Galaxies, and Beyond!

Modern astronomy encompasses a wide range of fascinating topics, from cutting-edge techniques used to detect and survey exosolar planets, to advances in astrophysics that reveal tantalizing glimpses into the nature of space and the beginning and possible end of our universe as a whole. This course will look at the tools and physics that astronomers utilize, as well as the electromagnetic spectrum to explore and expand our understanding of the Universe. Students will apply fundamental ideas from physics to the Sun, as well as distant objects, both within and outside our own Galaxy. *Three hours classroom, one two-hour laboratory a week. This course may count toward the astronomy minor.*

Attributes: Appropriate for First-Year, Lab Sciences, Quantitative Reasoning

205 The Physics of Life in the Universe

"Life", as we know it, is primarily composed of the elements carbon, hydrogen, oxygen, and nitrogen, along with phosphorus and sulfur. Where did these elements come from? How might they combine to produce "Life", and what do the laws of physics have to do with it all? We will begin our study with the Big Bang theory and the origin of the Universe and investigate the fundamental interactions that produced the first stars. We will consider the Early Earth and the conditions under which "Life" most likely formed. Do those conditions exist on other planets around other stars? What kind of physics is needed to detect "Life" on other planets? We will cover topics from nuclear, atomic, and molecular structure, to thermonuclear fusion in stars, to processes on the primordial Earth, as well as electromagnetic communication. Students taking this course will attend the same lectures as ASTR 105, but will have additional reading assignments and homework, and will be required to produce a final project in the course.*Prerequisite: PHYS 131 and 132 or 141 and 142. This course is cross-listed as PHYS 205.*

208 Introductory Astrophysics

An introduction to the physical basis of astronomy, including celestial mechanics and tools of observational astronomy. Insight into how the field has evolved since ancient times, as well as an appreciation of the problems explored by current research will be gained. Content is similar to ASTR 110, but with additional emphasis on mathematical analysis of astrophysical phenomena.

*Prerequisite: 131 or 141 or permission of instructor. This course is cross-listed as PHYS 208.*

306 Intermediate Astrophysics

This course covers in greater detail one area of astrophysics. The areas include stellar atmospheres and stellar magnetic fields, nuclear reactions, energy generation and nucleosynthesis in stars; the structure and content of galaxies; practical investigation and analysis of astrophysical phenomena using spectroscopy and the 24-inch Britton telescope, the programming language Python, and other data reduction tools; the structure and evolution of planetary surfaces and atmospheres.

*Prerequisite: 212 or permission of instructor. This course is cross-listed as PHYS 306.*

406 Advanced Astrophysics

An advanced course in selected areas of astrophysics. Topics selected from areas of astronomy and astrophysics that require a background in dynamics and electromagnetism. Topics may include celestial mechanics and orbit determination, numerical simulation of many-body systems, galactic dynamics, spectroscopy and electrodynamics of the interstellar medium, or general relativity and cosmology.

*Prerequisite: 311, 312 or permission of instructor. This course is cross-listed as PHYS 406.*

**Courses in Physics**

NOTE: Because of the similarity in course content, students will not receive graduation credit for both of the following pairs: 131 and 141, 132 and 142.

114 Climate Change and Renewable Energies

An introduction to the physics of global warming and a hands-on exploration of various types of renewable energy (RE), energy storage (ES), and ways to increase energy efficiency (EE). The first quarter of this project-centered course introduces the basic physical principles of global warming with a focus on radiative equilibrium, greenhouse effect, energy balance, and entropy. Since the energy sources of an energetically sustainable future will consist of renewable energies, the remaining three quarters of the course is devoted to an exploration of renewable energy solutions such as wind turbines, solar concentrators, and photovoltaic systems; energy storage solutions; and ways to increase the energy efficiency of buildings.

*This course will not count toward major requirements in physics. Offered every two years.*

Attributes: Appropriate for First-Year, ENST Applications (ESAP), Lab Sciences, Quantitative Reasoning, Sustainability Investigations

131 Workshop Physics: The Mechanical Universe

An introduction to classical mechanics using an inquiry-based, hands-on approach that combines cooperative learning with the use of computer tools for data acquisition, analysis, and mathematical modeling. Both analytic and numerical calculations are introduced for characterizing motion. A selection of kinesthetic experiments is included to enhance student learning. Topics include kinematics, Newton's laws of motion, gravitation, conservation laws, and rotational motion. Recommended for physical science, mathematics, and pre-engineering students and for biology majors preparing for graduate study. * Three two-hour sessions per week. Because of the similarity in course content, students will not receive graduation credit for both 131 and 141. Prerequisite: Completion of, or concurrent enrollment in, MATH 151 or 170. *

Attributes: Appropriate for First-Year, ENST Foundations (ESFN), Lab Sciences, Quantitative Reasoning

132 Workshop Physics: Matter and Fields

Workshop Physics: Matter and Fields
An introduction to thermal physics and electromagnetism using an inquiry-based, hands-on approach that combines cooperative learning with the use of computer tools for data acquisition, analysis, and mathematical modeling. Both analytic and numerical calculations are introduced for characterizing motion. A selection of kinesthetic experiments is included to enhance student learning. Topics include heat, temperature, phases of matter, kinetic theory, and heat engines; electric and magnetic fields, forces on charged particles, electrical circuits, and Ohm’s and Kirchhoff’s law; an introduction to Maxwell’s equations and electromagnetic waves.
*Three two-hour sessions per week. (Students enrolled in Physics 132 who have completed Mathematics 170 are encouraged to continue their mathematics preparation while taking physics by enrolling in Mathematics 171.) Because of the similarity in course content, students will not receive graduation credit for both 132 and 142. Prerequisite: 131 and completion of, or concurrent enrollment in MATH 170. *

Attributes: Appropriate for First-Year, ENST Foundations (ESFN), Lab Sciences, Quantitative Reasoning

141 Physics for the Life Sciences

Introductory, non-calculus physics, principally for life science and pre-med students. Topics include mechanics, fluid dynamics, thermodynamics.

* Three one-hour lectures and one three-hour lab per week. Because of the similarity in course content, students will not receive graduation credit for both 131 and 141.*

Attributes: ENST Foundations (ESFN), Lab Sciences, Quantitative Reasoning

142 Physics for the Life Sciences

Introductory, non-calculus physics, principally for life science and pre-med students. Topics include acoustics, optics, electricity, magnetism, and modern physics.

*Three one-hour lectures and one three-hour lab per week. Because of the similarity in course content, students will not receive graduation credit for both 132 and 142. Prerequisite: 141 or 131. *

Attributes: ENST Foundations (ESFN), Lab Sciences, Quantitative Reasoning

161 Introduction to Scientific Computing and Visualization

This half-credit course will introduce students to basic ideas and methods of scientific computing using a Python-based programming language. No prior knowledge of computer programming is required. Examples will draw heavily from classical mechanics, so some prior familiarity with introductory physics (or concurrent enrollment in PHYS 131) will be helpful but is not required. Topics range from projectile motion to planetary orbits, from collisions and scattering to oscillations. Other scientific explorations will be guided by student interest.

Attributes: Appropriate for First-Year

205 The Physics of Life in the Universe

"Life", as we know it, is primarily composed of the elements carbon, hydrogen, oxygen, and nitrogen, along with phosphorus and sulfur. Where did these elements come from? How might they combine to produce "Life", and what do the laws of physics have to do with it all? We will begin our study with the Big Bang theory and the origin of the Universe and investigate the fundamental interactions that produced the first stars. We will consider the Early Earth and the conditions under which "Life" most likely formed. Do those conditions exist on other planets around other stars? What kind of physics is needed to detect "Life" on other planets? We will cover topics from nuclear, atomic, and molecular structure, to thermonuclear fusion in stars, to processes on the primordial Earth, as well as electromagnetic communication. Students taking this course will attend the same lectures as ASTR 105, but will have additional reading assignments and homework, and will be required to produce a final project in the course.*Prerequisite: PHYS 131 and 132 or 141 and 142. This course is cross-listed as ASTR 205. *

208 Introductory Astrophysics

An introduction to the physical basis of astronomy, including celestial mechanics and tools of observational astronomy. Insight into how the field has evolved since ancient times, as well as an appreciation of the problems explored by current research will be gained. Content is similar to ASTR 110, but with additional emphasis on mathematical analysis of astrophysical phenomena.

*Prerequisite: 131 or 141 or permission of instructor. This course is cross-listed as ASTR 208. *

211 Vibrations, Waves & Optics

The physics of periodic motions, oscillating systems, resonances, propagating waves and optical phenomena. The course is centered around various projects such as the investigation of a kinetic art apparatus, the study of a tuned-mass-damper in a high-rise building, an examination of the Fourier spectrum of different musical instruments, and the dispersion relation for a very large slinky. The course culminates with a presentation at either the "Rainbow Symposium" or the "Vision Symposium."

*Prerequisite: 131 and 132 or 131 and 142, and completion of, or concurrent enrollment in, MATH 171 or permission of instructor. NOTE: Completion of both 211 and 212 fulfills the WID requirement.*

Attributes: Lab Sciences

212 Introduction to Relativistic and Quantum Physics

A project-based course focusing on special relativity and quantum physics. Projects, such as the detection and measurement of ionizing radiation, relativistic mass increase, or the investigation of delayed choice experiments, are used to understand the concepts of the atom, nuclear structure, relativity, and quantum mechanics.

*Prerequisite: 132 or 142, and Math 171 or permission of instructor. NOTE: Completion of both 211 and 212 fulfills the WID graduation requirement. *

213 Analog & Digital Electronics

Circuit design and the analysis of electronic devices. Modern digital and analog circuit elements, including diodes, transistors, op amps, and various integrated circuits, are used in amplifiers, power supplies, and logic circuits. Class and laboratory work are integrated during class time totaling up to seven hours per week. Students design and build projects at the end of the semester.

*Prerequisite: 132 or 142, and completion of, or concurrent enrollment in, MATH 171 or permission of instructor. *

Attributes: Lab Sciences

282 Introduction to Theoretical Physics

A rigorous survey of mathematical topics and techniques that are commonly used in theoretical physics. Topics include vector analysis, differential equations, power series, linear algebra, tensors, and vector calculus (gradient, divergence, curl, line integrals, and so on). The primary focus of this course is on solving problems as a means to improve students’ confidence and understanding of mathematics within the context of physical systems.

*Prerequisite: 132 and MATH 171.*

306 Intermediate Astrophysics

This course covers in greater detail one area of astrophysics. The areas include stellar atmospheres and stellar magnetic fields, nuclear reactions, energy generation and nucleosynthesis in stars; the structure and content of galaxies; practical investigation and analysis of astrophysical phenomena using spectroscopy and the 24-inch Britton telescope, the programming language Python, and other data reduction tools; the structure and evolution of planetary surfaces and atmospheres.

*Prerequisite: 212 or permission of instructor. This course is cross-listed as ASTR 306. *

311 Dynamics & Chaos

An advanced treatment of classical mechanics using vector calculus and the calculus of variations, as well as an introduction to the analysis of chaotic systems. Topics will include: the dynamics of systems of particles and conservation laws; linear and nonlinear oscillators; iterative maps and the route to chaos; central force motion; rigid body motion; non-inertial reference frames and fictitious forces; Lagrangian and Hamiltonian formulations of dynamics. The course will also focus heavily on analytical and problem-solving techniques.

*Prerequisite: 211 and 282 or permission of the instructor. *

312 Electrodynamics

This course will investigate electrostatics, magnetostatics, and electrodynamics in vacuum and in matter. Maxwell's equations of electrodynamics are developed and explored in depth. Vector calculus is used throughout this course. Possible projects include the experimental study of capacitors, the force and torque on a magnetic dipole, and an exploration of Faraday-induced electric fields.

*Prerequisite: 211, 212 and 282, or permission of instructor. *

313 Computer Interfacing and Laboratory Instrumentation

A study of the interfacing techniques needed for data acquisition and the control of laboratory equipment. An introduction to the LabView programming environment and how it can be used to automate typical laboratory tasks, for example, the control of linear or rotational actuators or the measurement and analysis of audio signals.

*Prerequisite: 213 or permission of instructor. Offered occasionally.*

314 Renewable Energy Engineering

A project-centered approach to the study of renewable energy sources, energy storage, and energy efficiency. Examples of projects include: the Solar Air Heater (SAH), Evacuated Tube Solar Collectors, Photovoltaic (PV) Arrays, Thermal Storage Devices based on Phase Change Materials (PCMs), LED lighting, modern wind turbines, adiabatic compression and expansion, and the coefficient of performance (COP) of heat pumps. In particular, students design, build, test, and re-engineer their own SAH with an absorber based on physics principles learned in the course.

*Prerequisite: 131 and 132 or 141 and 142, and 211 or permission of instructor. Offered every two years. *

Attributes: ENST Applications (ESAP), Sustainability Investigations

315 Principles of Medical Imaging

This course will examine the physical principles that allow physicians to look inside the human body and will investigate how these principles are implemented in practice. This course will cover the following topics: Magnetic Resonance Imaging (MRI), medical ultrasound, Positron Emission Tomography (PET), lasers in medicine, and medical X-rays. It will involve some hands-on demos or projects.

*Prerequisite: 211 and 212 and MATH 171 or permission of instructor. Normally offered every other year.*

331 Thermodynamics and Statistical Mechanics

The basic laws of thermodynamics are derived from principles of statistical mechanics. Thus, the laws governing our macroscopic world are seen as fundamentally statistical in nature. Familiar quantities, like temperature and pressure, will be re-discovered, and new ones, like entropy and free energy, will be developed and applied to real-world problems in engineering, condensed-matter physics, and chemistry. We will conclude with an examination of phase transitions and quantum statistics.

*Prerequisite: 211 and 212 and 282. Offered every two years.*

361 Topics in Modern Physics

Topics to be selected from areas such as atomic, nuclear, or solid state physics; or modern optics, fluid dynamics, plasma or computational physics.

*Prerequisite: 211 and 212. One-half or one course credit.*

392 Contemporary Topics and Careers in Physics and Astronomy

This seminar examines physics and astronomy as contemporary research disciplines, their divisions into broad subfields, as well as some research questions of current importance. A second emphasis is on the development of bibliographic and scientific presentation skills. The seminar also familiarizes students with the application process for internships and research experiences. Finally, it prepares physics and astronomy majors for life after Dickinson (career options, graduate programs, cover letters, personal statements, etc.).

*Prerequisite: Physics major junior status. One-half course credit.*

406 Advanced Astrophysics

An advanced course in selected areas of astrophysics. Topics selected from areas of astronomy and astrophysics that require a background in dynamics and electromagnetism. Topics may include celestial mechanics and orbit determination, numerical simulation of many-body systems, galactic dynamics, spectroscopy and electrodynamics of the interstellar medium, or general relativity and cosmology.

*Prerequisite: 311, 312 or permission of instructor. This course is cross-listed as PHYS 406. *

412 Advanced Electrodynamics and Plasmas

A continuation of the topics covered in Physics 312 with an emphasis on electromagnetic waves in air, in conductors, and in space plasmas. Possible projects include the reflection and transmission of electromagnetic waves at an interface, waveguides, plasma waves in space, electromagnetic radiation from antennas, and the equilibrium and stability of plasmas.

*Prerequisite: 312 or permission of instructor. Offered only occasionally.*

431 Quantum Mechanics

Basic postulates are used to develop the theoretical framework for quantum mechanics. The course deals with measurements on quantum systems, the uncertainty principle, the Schrödinger wave equation and the probability interpretation, Heisenberg's matrix mechanics, eigenfunctions and eigenvalues, finite and infinite dimensional vector spaces, operator methods, and enables students to use the Dirac formalism for quantum mechanical manipulations for a variety of situations and systems. *Prerequisites: 212 and 282 and at least one 300-level physics course, or permission of instructor. Normally offered every other year*

491 Advanced Laboratory Capstone I

In this capstone experience, students will work in groups to study several advanced physics topics in detail. Potential topics include muon decay, microwave diffraction, the speed of light, pulsed nuclear magnetic resonance, and the Hall effect. The course emphasizes collaborative research, investigative techniques, oral and written communication.

*Prerequisite: Physics major senior status. The physics major requires either the two-semester sequence of 491 & 492 OR two semesters of PHYS 550.*

492 Advanced Laboratory Capstone II

In this capstone experience, students will work in groups to study several advanced physics topics in detail. Potential topics include muon decay, microwave diffraction, the speed of light, pulsed nuclear magnetic resonance, and the Hall effect. The course emphasizes collaborative research, investigative techniques, oral and written communication.*Prerequisite: Physics major senior status. The physics major requires either the two-semester sequence of 491 & 492 OR two semesters of PHYS 550.
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