- Demonstrate the ability to use basic mathematical tools (algebra, basic differential and/or integral calculus, trigonometry, geometry) to describe physical situations, whether experimental or theoretical (all sub-1100 courses focus on this).
- Explore the relationship between physical theory and experiment, through mathematical descriptions and instrument-based verification.
- Improve understanding of physical law through the ability to solve increasingly complex problems in physics, with more complex mathematical tools (multivariate calculus, differential equations, linear algebra, and more complex math tools).
- Demonstrate the ability to use sophisticated instrumentation to explore physical phenomena (including computation).
- Throughout the various levels of the curriculum, students will improve their understanding of uncertainty and its key role in defining how we know what we know.
- Focus on expanding tools and techniques in either theoretical physics or experimental physics (or both) at the 3000 level.

# Physics and Astronomy

## Learning Goals

An undergraduate major in physics should give a graduating student a basic understanding of the four basic interactions, and provide them with an array of mathematical tools and experimental tools to explore physical phenomena involving those interactions.

Our curriculum is set up to continually test the student’s ability to use these tools to analyze physical situations. The complexity of the material builds, with analysis at any level (1000, 2000, 3000) relying on the material at a lower level as a base starting point.

### The Six Learning Goals:

Stephen G. Naculich, *Department Chair*

Emily C. Briley, *Department Coordinator*

*Professors:* Mark O. Battle, Thomas Baumgarte, Elizabeth F. McCormack, Madeleine E. Msall, Stephen G. Naculich, Dale A. Syphers‡

*Senior Lecturer:* Karen Topp

*Visiting Faculty:* Jeff Hyde

*Laboratory Instructors:* Kenneth Dennison, Paul Howell, Gary L. Miers

## Physics Major

The major requires nine courses.

Code | Title | Credits |
---|---|---|

Required Courses | ||

Mathematics through 1700, or placement above 1700 | 1 | |

PHYS 1130 | Introductory Physics I (or placement above 1130) | 1 |

PHYS 1140 | Introductory Physics II | 1 |

PHYS 2130 | Electric Fields and Circuits | 1 |

PHYS 2140 | Quantum Physics and Relativity | 1 |

PHYS 2150 | Statistical Physics | 1 |

Select one of the following advanced methods courses: | 1 | |

Methods of Theoretical Physics | ||

Methods of Experimental Physics | ||

Methods of Computational Physics | ||

Select two additional approved courses higher than 1140. ^{a} | 2 |

In addition to the requirements listed above, students pursuing honors are expected to take MATH 1800 Multivariate Calculus, PHYS 3000 Methods of Theoretical Physics, and PHYS 4050 Physics Honor Project. At least three courses taken for the major with honors must be at the advanced level, 3000–3999.

a |

## Physics Minor

The minor consists of at least four physics courses (completed at Bowdoin) numbered 1130 or higher, one of which must be PHYS 1140 Introductory Physics II.

## Interdisciplinary Majors

The department participates in interdisciplinary programs in chemical physics and physics and education. See the Interdisciplinary Majors.

## Additional Information and Department Policies

- Students must earn a grade of C- or above in any prerequisite physics course. Up to two courses with a grade of D are allowed to be counted toward the major if they are not prerequisites.
- Majors must complete at least five physics courses at Bowdoin.
- Courses that count toward the major or minor must be taken for regular letter grades (not Credit/D/Fail).
- Students interested in applying coursework taken at another college or university to the major or minor should consult the department.
- Independent studies, including honors projects, may count toward the major or minor.
- Advanced Placement/International Baccalaureate (AP/IB):
- Students who receive a minimum score of four on the Physics 1 AP exam are exempt from taking PHYS 1130 Introductory Physics I, and do not need to take an additional course to replace it. No AP credit is awarded for the Physics 2 AP exam.
- Students who receive a minimum score of four on the Physics C: Mechanics AP exam or a minimum score of six on the Physics without Optics IB exam are eligible to receive one credit toward the major, are exempt from taking PHYS 1130 Introductory Physics I, and are placed in PHYS 1140 Introductory Physics II. To earn the credit, a minimum grade of C- (not taken Credit/D/Fail) must be received in PHYS 1140 Introductory Physics II by the end of their junior year or no credit is awarded. Students who receive a minimum score of six on the Physics with Optics IB exam are eligible to receive one credit toward the major and have the option of being placed in either PHYS 1140 Introductory Physics II or PHYS 2130 Electric Fields and Circuits. To receive the credit, the student must earn a minimum grade of C- (not taken Credit/D/Fail) in the course in which they choose to be placed, and it must be completed by the end of their junior year.
- Minors meeting either of the criteria above are exempt from taking PHYS 1130 Introductory Physics I, but must take at least four Bowdoin physics courses.
- No credit is awarded for the Physics 2 or Physics C: Electricity and Magnetism AP exams.
- In order to receive credit for AP/IB work, students must have their scores officially reported to the Office of the Registrar by the end of their sophomore year at Bowdoin.

- The major program depends to some extent on the student’s goals, which should be discussed with the department. Those who intend to do graduate work in physics or an allied field should plan to do an honors project.
- Students considering a program in engineering should consult the Special Areas of Study.
- A major with an interest in an interdisciplinary area such as geophysics, biophysics, or oceanography should choose appropriate courses in related departments.
- Secondary school teaching requires a broad base in science courses, as well as the necessary courses for teacher certification. Students who know they want to do this should consider the physics and education interdisciplinary major.
- For a career in industrial management, some courses in economics and government should be included.

### Interdisciplinary Majors

The Department of Physics and Astronomy participates in an interdisciplinary major, Chemical Physics, with the Department of Chemistry as well as an interdisciplinary major, Physics and Education, with the Department of Education. See the Interdisciplinary Majors section for more information. In addition, students are able to declare a coordinate major between Physics and either Education or Environmental Studies as well. The department does not explicitly participate in a formal interdisciplinary program with the Department of Earth and Oceanographic Science. However, the Departments of Physics and Earth and Oceanographic Science have identified major/minor pathways for students interested in majoring in physics with an earth and oceanographic science application (physics major/earth and oceanographic science minor) and students interested in majoring in earth and oceanographic science with a physics application (earth and oceanographic science major/physics minor).

Students pursuing the physics major/earth and oceanographic science minor with interests in the solid earth discipline would be best served by selecting:

Code | Title | Credits |
---|---|---|

EOS 1105 | Investigating Earth | 1 |

EOS 2005/ENVS 2221 | Biogeochemistry: An Analysis of Global Change | 1 |

Select two of the following: | 2 | |

Field Studies in Structural Geology | ||

The Plate Tectonics Revolution | ||

Geomechanics and Numerical Modeling | ||

Mountains to Trenches: Petrology and Process | ||

Research in Mineral Science |

Those with interests in the surface earth discipline should select:

Code | Title | Credits |
---|---|---|

EOS 1305/ENVS 1104 | Environmental Geology and Hydrology | 1 |

EOS 2005/ENVS 2221 | Biogeochemistry: An Analysis of Global Change | 1 |

EOS 2325 | Environmental Chemistry | 1 |

EOS 2345/ENVS 2270 | Geomorphology: Form and Process at the Earth's Surface | 1 |

Those with interests in the oceanography discipline should choose:

Code | Title | Credits |
---|---|---|

EOS 1505 | Oceanography | 1 |

EOS 2005/ENVS 2221 | Biogeochemistry: An Analysis of Global Change | 1 |

Select two of the following: | ||

Marine Biogeochemistry | ||

Poles Apart: Exploration of Earth’s High Latitudes | ||

Equatorial Oceanography | ||

Satellite Remote Sensing of the Ocean | ||

Ocean and Climate | ||

Research in Oceanography: Topics in Paleoceanography |

### Physics and 3-2 Engineering

Students planning to pursue one of the 3-2 engineering options and graduating with a physics degree must take:

Code | Title | Credits |
---|---|---|

PHYS 1140 | Introductory Physics II | 1 |

PHYS 2130 | Electric Fields and Circuits | 1 |

PHYS 2150 | Statistical Physics | 1 |

PHYS 3000 | Methods of Theoretical Physics | 1 |

or MATH 2208 | Ordinary Differential Equations | |

CHEM 1102 | Introductory Chemistry II | 1 |

or CHEM 1109 | General Chemistry | |

MATH 1800 or higher | ||

CSCI 1101 | Introduction to Computer Science | 1 |

Other courses are expected by the partnering engineering institution and students should contact the advisor in Bowdoin's Department of Physics and Astronomy for more information.

**PHYS 1082** **(a, INS, MCSR) ** **Physics of Musical Sound**

Every Other Fall. Fall 2019. Enrollment limit: 30.

An introduction to the physics of sound, specifically relating to the production and perception of music. Topics include simple vibrating systems; waves and wave propagation; resonance; understanding intervals, scales, and tuning; sound intensity and measurement; sound spectra; how various musical instruments and the human voice work. Students expected to have some familiarity with basic musical concepts such as scales and intervals. Students with musical experience who have not taken the music placement test, nor registered for any music ensemble or lesson as listed in the prerequisites, may e-mail ktopp@bowdoin.edu with a quick description of their musical background. Not open to students who have credit for or are concurrently taking any physics course numbered 1100 or higher.

Prerequisites: MUS 1051 or Placement in MUS 1401 or Placement in MUS 2403 or MUS 1801 - 1878 or MUS 2701 - 2752 or MUS 2769 - 2779 or MUS 2783 or MUS 2801 - 2878.

Previous terms offered: Fall 2017, Fall 2015.

**PHYS 1083** **(a, INS, MCSR) ** **Energy, Physics, and Technology**

How much can we do to reduce the disruptions of the Earth’s physical, ecological, and social systems caused by global climate change? How much climate change itself can we avoid? A lot depends on the physical processes that govern the extraction, transmission, storage, and use of available energy. Introduces the physics of solar, wind, nuclear, and hydroelectric power and discusses the physical constraints on their efficiency, productivity, and safety. Reviews current technology and quantitatively analyzes the effectiveness of different strategies to reduce greenhouse gas emissions. Not open to students with credit for Physics 1140. (Same as: ENVS 1083)

Previous terms offered: Spring 2019, Spring 2016.

**PHYS 1087** **(a, INS) ** **Building a Sustainable World**

The big problems of the world are enormously complex and pose daunting challenges for current and future generations. Climate change, pollution, energy, and nuclear power are only a few of the increasingly critical issues. A leader--whether a president or a teacher, in Congress or in the media, in business or as a voter--needs to understand not only the science and technology that underlie the problems and possible solutions, but also how science defines and pursues a problem, engages in debate, and communicates with the public. In addition to lectures, classes structured as discussions and small working groups.

Previous terms offered: Spring 2018, Fall 2016.

**PHYS 1093** **(a, MCSR) ** **Introduction to Quantitative Reasoning in the Physical Sciences**

Climate science. Quantum Physics. Bioengineering. Rocket science. Who can understand it? Anyone with high school mathematics (geometry and algebra) can start. Getting started in physics requires an ability to mathematically describe real world objects and experiences. Prepares students for additional work in physical science and engineering by focused practice in quantitative description, interpretation, and calculation. Includes hands-on measurements, some introductory computer programming, and many questions about the physics all around us. Registration for this course is by placement only. To ensure proper placement, students must have taken the physics placement examination prior to registering for Physics 1093. (Same as: CHEM 1093)

Prerequisites: Placement in PHYS 1093.

Previous terms offered: Fall 2018, Fall 2017, Fall 2016, Fall 2015.

**PHYS 1130** **(a, INS, MCSR) ** **Introductory Physics I**

Every Semester. Fall 2019. Enrollment limit: 50.

An introduction to the conservation laws, forces, and interactions that govern the dynamics of particles and systems. Shows how a small set of fundamental principles and interactions allow us to model a wide variety of physical situations, using both classical and modern concepts. A prime goal of the course is to have the participants learn to actively connect the concepts with the modeling process. Three hours of laboratory work per week. To ensure proper placement, students are expected to have taken the physics placement examination prior to registering for Physics 1130.

Prerequisites: Two of: MATH 1600 or higher or Placement in MATH 1700 (M) or Placement in MATH 1750 (M) or Placement in MATH 1800 (M) or Placement in 2000, 2020, 2206 (M) and PHYS 1093 or Placement in PHYS 1130.

Previous terms offered: Spring 2019, Fall 2018, Spring 2018, Fall 2017, Spring 2017, Fall 2016, Spring 2016, Fall 2015.

**PHYS 1140** **(a, INS, MCSR) ** **Introductory Physics II**

Every Semester. Fall 2019. Enrollment limit: 50.

An introduction to the interactions of matter and radiation. Topics include the classical and quantum physics of electromagnetic radiation and its interaction with matter, quantum properties of atoms, and atomic and nuclear spectra. Laboratory work (three hours per week) includes an introduction to the use of electronic instrumentation.

Prerequisites: Two of: MATH 1700 - 1800 or Placement in MATH 1800 (M) or Placement in 2000, 2020, 2206 (M) and PHYS 1130 or Placement in PHYS 1140.

Previous terms offered: Spring 2019, Fall 2018, Spring 2018, Fall 2017, Spring 2017, Fall 2016, Spring 2016, Fall 2015.

**PHYS 1510** **(a, INS, MCSR) ** **Introductory Astronomy**

Every Spring. Fall 2019. Enrollment limit: 50.

A quantitative introduction to astronomy with emphasis on stars and the structures they form, from binaries to galaxies. Topics include the night sky, the solar system, stellar structure and evolution, white dwarfs, neutron stars, black holes, and the expansion of the universe. Several nighttime observing sessions required. Does not satisfy pre-med or other science departments’ requirements for a second course in physics.

Prerequisites: MATH 1600 or higher or Placement in MATH 1700 (M) or Placement in MATH 1750 (M) or Placement in MATH 1800 (M) or Placement in 2000, 2020, 2206 (M).

Previous terms offered: Fall 2018, Fall 2017, Spring 2017, Spring 2016.

**PHYS 2130** **(a, INS, MCSR) ** **Electric Fields and Circuits**

Every Fall. Fall 2019. Enrollment limit: 30.

The basic phenomena of the electromagnetic interaction are introduced. The basic relations are then specialized for a more detailed study of linear circuit theory. Laboratory work stresses the fundamentals of electronic instrumentation and measurement with basic circuit components such as resistors, capacitors, inductors, diodes, and transistors. Three hours of laboratory work per week.

Prerequisites: PHYS 1140.

Previous terms offered: Fall 2018, Fall 2017, Fall 2016, Fall 2015.

**PHYS 2140** **(a, INS, MCSR) ** **Quantum Physics and Relativity**

An introduction to two cornerstones of twentieth-century physics, quantum mechanics, and special relativity. The introduction to wave mechanics includes solutions to the time-independent Schrödinger equation in one and three dimensions with applications. Topics in relativity include the Galilean and Einsteinian principles of relativity, the “paradoxes” of special relativity, Lorentz transformations, space-time invariants, and the relativistic dynamics of particles. Not open to students who have credit for or are concurrently taking Physics 3140 or 3500.

Prerequisites: PHYS 1140.

Previous terms offered: Spring 2019, Spring 2018, Spring 2017, Spring 2016.

**PHYS 2150** **(a, INS, MCSR) ** **Statistical Physics**

Develops a framework capable of predicting the properties of systems with many particles. This framework, combined with simple atomic and molecular models, leads to an understanding of such concepts as entropy, temperature, and chemical potential. Some probability theory is developed as a mathematical tool.

Prerequisites: PHYS 1140.

Previous terms offered: Spring 2019, Spring 2018, Spring 2017, Spring 2016.

**PHYS 2220** **(a, INS, MCSR) ** **Engineering Physics**

Examines the physics of materials from an engineering viewpoint, with attention to the concepts of stress, strain, shear, torsion, bending moments, deformation of materials, and other applications of physics to real materials, with an emphasis on their structural properties. Also covers recent advances, such as applying these physics concepts to ultra-small materials in nano-machines. Intended for physics majors and architecture students with an interest in civil or mechanical engineering or applied materials science.

Prerequisites: PHYS 1140.

Previous terms offered: Fall 2017, Spring 2016.

**PHYS 2230** **(a, INS, MCSR) ** **Modern Electronics**

A brief introduction to the physics of semiconductors and semiconductor devices, culminating in an understanding of the structure of integrated circuits. Topics include a description of currently available integrated circuits for analog and digital applications and their use in modern electronic instrumentation. Weekly laboratory exercises with integrated circuits.

Prerequisites: PHYS 1130 or PHYS 1140.

Previous terms offered: Spring 2019, Spring 2017.

**PHYS 2240** **(a, INS, MCSR) ** **Acoustics**

An introduction to the motion and propagation of sound waves. Covers selected topics related to normal modes of sound waves in enclosed spaces, noise, acoustical measurements, the ear and hearing, phase relationships between sound waves, and many others, providing a technical understanding of our aural experiences.

Prerequisites: PHYS 1140.

Previous terms offered: Fall 2018, Fall 2016.

**PHYS 2250** **(a, INS, MCSR) ** **Physics of Solids**

Solid state physics describes the microscopic origin of the thermal, mechanical, electrical and magnetic properties of solids. Examines trends in the behavior of materials and evaluates the success of classical and semi-classical solid state models in explaining these trends and in predicting material properties. Applications include solid state lasers, semiconductor devices, and superconductivity. Intended for physics, chemistry, or earth and oceanographic science majors with an interest in materials physics or electrical engineering.

Prerequisites: PHYS 2140 or CHEM 2520.

Previous terms offered: Spring 2018, Spring 2016.

**PHYS 2260** **(a, INS, MCSR) ** **Nuclear and Particle Physics**

An introduction to the physics of subatomic systems, with a particular emphasis on the standard model of elementary particles and their interactions. Basic concepts in quantum mechanics and special relativity are introduced as needed.

Prerequisites: PHYS 2140.

Previous terms offered: Spring 2019, Spring 2017.

**PHYS 2410** **(a, INS, MCSR) ** **Accident Reconstruction: Physics, The Common Good, and Justice**

Introduces the applications of physics pertinent to accident reconstruction and analyzes three complex cases that were criminal prosecutions. Instructor analyzes the first case to show how the physics is applied, the second is done in tandem with students, and the third is mostly analyzed by the students,using what they have learned. The report on this third case serves as the final project for the course. While Physics 1130 is the only prerequisite for the course, familiarity with vectors and matrices, or a desire to learn how to use them, is necessary.

Prerequisites: PHYS 1130.

Previous terms offered: Fall 2018, Fall 2015.

**PHYS 2510** **(a) ** **Astrophysics**

**PHYS 2810** **(a, INS, MCSR) ** **Atmospheric and Ocean Dynamics**

A mathematically rigorous analysis of the motions of the atmosphere and oceans on a variety of spatial and temporal scales. Covers fluid dynamics in inertial and rotating reference frames, as well as global and local energy balance, applied to the coupled ocean-atmosphere system. (Same as: ENVS 2253, EOS 2810)

Prerequisites: PHYS 1140.

Previous terms offered: Fall 2017, Fall 2015.

**PHYS 2900** **(a, INS, MCSR) ** **Topics in Contemporary Physics**

Non-Standard Rotation. Fall 2019. Enrollment limit: 35. .5 Credit Credit/D/F Only.

**PHYS 3000** **(a, INS, MCSR) ** **Methods of Theoretical Physics**

Every Fall. Fall 2019. Enrollment limit: 20.

Mathematics is the language of physics. Similar mathematical techniques occur in different areas of physics. A physical situation may first be expressed in mathematical terms, usually in the form of a differential or integral equation. After the formal mathematical solution is obtained, the physical conditions determine the physically viable result. Examples are drawn from heat flow, gravitational fields, and electrostatic fields.

Prerequisites: Two of: either PHYS 2130 or PHYS 2140 or PHYS 2150 and MATH 1800 or Placement in 2000, 2020, 2206 (M).

Previous terms offered: Fall 2018, Fall 2017, Fall 2016, Fall 2015.

**PHYS 3010** **(a, INS, MCSR) ** **Methods of Experimental Physics**

Intended to provide advanced students with experience in the design, execution, and analysis of laboratory experiments. Projects in optical holography, nuclear physics, cryogenics, and materials physics are developed by the students.

Prerequisites: PHYS 2130.

Previous terms offered: Spring 2019, Spring 2018, Spring 2017, Spring 2016.

**PHYS 3020** **(a, INS, MCSR) ** **Methods of Computational Physics**

Every Other Fall. Fall 2019. Enrollment limit: 20.

An introduction to the use of computers to solve problems in physics. Problems are drawn from several different branches of physics, including mechanics, hydrodynamics, electromagnetism, and astrophysics. Numerical methods discussed include the solving of linear algebra and eigenvalue problems, ordinary and partial differential equations, and Monte Carlo techniques. Basic knowledge of a programming language is expected.

Prerequisites: Two of: either CSCI 1101 or Placement in above CSCI 1101 or CSCI 1103 and PHYS 1140.

Previous terms offered: Fall 2017, Fall 2015.

**PHYS 3120** **(a, INS, MCSR) ** **Advanced Mechanics**

A thorough review of particle dynamics, followed by the development of Lagrange’s and Hamilton’s equations and their applications to rigid body motion and the oscillations of coupled systems.

Prerequisites: PHYS 3000.

Previous terms offered: Spring 2018, Spring 2017.

**PHYS 3130** **(a) ** **Electromagnetic Theory**

**PHYS 3140** **(a, INS, MCSR) ** **Quantum Mechanics**

Every Fall. Fall 2019. Enrollment limit: 20.

A mathematically rigorous development of quantum mechanics, emphasizing the vector space structure of the theory through the use of Dirac bracket notation. Linear algebra developed as needed.

Prerequisites: Two of: PHYS 2140 and PHYS 3000.

Previous terms offered: Fall 2018, Fall 2017, Fall 2016, Fall 2015.

**PHYS 3200** **(a, MCSR) ** **Fields, Particles, and Symmetries**

An introduction to the theory of relativistic quantum fields, the foundational entities of the standard model of elementary particle physics. Topics include Lagrangian formulation of the classical mechanics of particles and fields, Noether's theorem relating symmetries to conservation laws, the quantization of bosonic and fermionic fields, the role of abelian and non-abelian gauge symmetries in determining the form of interactions among elementary particles, the use of Feynman diagrams to compute elementary processes, the spontaneous breaking of symmetry, and the Higgs mechanism.

Prerequisites: Two of: PHYS 2140 and PHYS 3000.

Previous terms offered: Fall 2016.

**PHYS 3500** **(a, INS, MCSR) ** **General Relativity**

First discusses special relativity, introducing the concept of four-dimensional space-time. Then develops the mathematical tools to describe space-time curvature, leading to the formulation of Einstein’s equations of general relativity. Finishes by studying some of the most important astrophysical consequences of general relativity, including black holes, neutron stars, and gravitational radiation.

Prerequisites: Two of: PHYS 2140 and PHYS 3000.

Previous terms offered: Spring 2017.