# Physics Curriculum

Here's an overview of the major and minor requirements, as well as the courses offered in this department. While there's an incredible list of classes you can choose from, take what you know you have time for (students typically take 2-3 technical classes a semester, but it depends on the person). Before choosing a class, check Berkeley Time for previous grade distributions, visit RateMyProfessor or ask around for Professor reviews, and check class syllabuses especially for electives!

## How to Major/Minor

### Declaring

One can declare the Major after completing 30 units of courses, which must include the required lower division courses listed below, with a GPA of at least 2.0, as well as having an overall university GPA of at least 2.0. Please see lower division requirements for more details on the required classes to declare.

The requirements required to declare the minor is the same as that of the major. See below:

**Lower division course requirements to declare Major/Minor:**

- Physics 5 series or Physics 7 series
- Physics 5A, 5B & 5BL, and 5C & 5CL
- OR Physics 7A, 7B, and 7C

- Math 1A
- Math 1B
- Math 53
- Physics 89

### Majoring

To complete the major, one must complete the upper division requirements, as well as one elective. The upper division course requirements and elective can be taken in any order.

**Upper division course requirements for the major:**

- Physics 110A
- Physics 111A
- Physics 111B
- Physics 112
- Physics 137A
- Physics 137B
- One upper division course elective

### Minoring

Once the minor has been declared, the following corses must be taken for a letter grade to complete it.

**Upper division course requirements for the minor:**

- Physics 137A
- Physics 110A or Physics 105
- Three additional upper division physics courses (to total at least 9 units, for an upper division physics unit total of at least 17 units).

## Lower Division Course Requirements

The physics major requires the completion of one of the introductory physics sequences, either the **Physics 7 series** or the **Physics 5 series**, as well as **Physics 89**. Students can switch between the 5 series and the 7 series, but because it isn't one-to-one, is recommended that you talk to a major advisor and the professor teaching it first.

The **Physics 7 Series** comprises Physics 7A, Physics 7B, and Physics 7C, and is the standard introductory physics sequence for science and engineering majors. Physics 7A presents a basic introduction to Newtonian mechanics, Physics 7B is split between classical thermodynamics and electromagnetism, and Physics 7C describes optics, special relativity, and quantum mechanics. For homework assignments, the Physics 7 series utilizes MasteringPhysics, an online web application for physics problems. The Physics 7 series is focused more on computational details than the theory behind the subject. Each course contains a lab component within the course.

The **Physics 5 Series** comprises Physics 5A, Physics 5B/Physics 5BL, and Physics 5C/Physics 5CL, and is the honors introductory physics sequence specifically geared towards physics majors. 5 Series courses tend to be smaller in size and also mostly attended by intended physics majors. The curriculum for the 5 Series is somewhat different than that of the 7 Series. Physics 5A describes classical mechanics and special relativity. Physics 5B focuses on electromagnetism, waves, and optics. Physics 5C mostly involves quantum mechanics and statistical mechanics, a more fundamental treatment of thermodynamics. The 5 Series tends to be more theoretical and rigorous, but provides a very strong foundation for upper division coursework. While Physics 5A has no lab component, Physics 5B and 5C are accompanied by separate, companion lab courses Physics 5BL and 5CL, which are more comprehensive introductions to experimental physics culminating in a capstone project in 5CL.

**Physics 89** is the lower division introduction to mathematical physics, including linear algebra, complex numbers, tensors, and differential equations. Physics 89 cannot be substituted by any linear algebra class except for Math 54, and only then in cases where there is a double major with mathematics.

**Physics 77** (Not a major requirement, but strongly recommended) is an introductory course to programming in Python. There you learn the basics of Python and NumPy, along with a few techniques related to computational techniques. It isn't much, but it is a really good introduction to the kind of coding that you might do for your research. Note that this class is not required for the major, but strongly recommended.

## Upper Division Course Requirements

Physics 105 may sound like a rehashing of lower division classical mechanics but, at its heart, is a fundamentally groundbreaking course. Students explore the Lagrangian and Hamiltonian formulations of classical mechanics which apply the curiously named “principle of least action” to transform the messy vector equations of Newtonian vector mechanics into the elegant scalar relations of analytic mechanics. Students will see how the centrifugal and Coriolis forces fall beautifully out of the math of rotating frames, how central force potentials manifest as gravitational orbits, and how vibrations and rotations can be treated under this new analytical framework. Instructors also often introduce the basic concepts of chaos theory, a field which attempts to describe systems whose dynamics are extremely sensitive to initial conditions. This course is a must-have for even the least classical-sounding physics fields out there.

*Prior to taking this class, completion of 5A/7A is strongly recommended.*

This course is essentially an extension of the lower division electrodynamics of Physics 5B/7B. In this class, students will make a significantly deeper dive into the apparently familiar theory of electromagnetism through a higher level of vector calculus. The class explores in depth the macroscopic formulation of Maxwell’s equations which describe the laws of electrodynamics in realistic materials that respond to electromagnetic fields. The familiar electric and magnetic fields can be thought to arise from scalar and vector potential functions which introduce the fancy-sounding concept of a “gauge theory.” On this note, the class segues into a more rigorous exploration of special relativity in a way that reveals the deeper geometrical interpretation of the theory.

*Prior to taking this class, completion of 5B/7B is strongly recommended.*

Physics 111A, previously 111BSC (basic semiconductor circuits), has a notorious reputation for the vast amount of time it requires. With (or without) a partner, students learn the basic theory behind increasingly complicated circuits while heading into the Donald A. Glaser laboratory on the second floor to put those theoretical ideas to practice. While in the class, students will learn to produce and readout signal parameters. It is impossible to come away from the course without a reasonable understanding of diodes (which “pump” current in one direction), JFET and BJT transistors (the basis of switches), op amps (which magnify voltages insanely), and analog/digital logic. The course also introduces students to the National Instruments software LabVIEW, which is used in countless physics labs across the world. The course culminates in a final project where students’ creativity and circuit-building prowess are put to the test. As a rite of passage of the physics major, one should heed the warning/advocacy: tread wisely.

*Prerequisite is the lower division lab classes.*

In Physics 111B, previously 111ADV (advanced laboratory), students are given 4 physics experiments to do throughout the semester. These experiments closely resemble those performed in actual physics research. For each experiment, a report, complete with a theory outline, procedure, data analysis (including full error analysis) must be completed. For this class, time management is key, as the course takes an amount of time comparable to the infamous Physics 111A, but is far less structured.

*Prerequisite is 111A.*

Physics 112, or Statistical Mechanics is all about the physics of many particles. Many of the problems that you saw in your introductory physics classes involve only a few bodies in motion, like a ball rolling down a plane or a charge from a rod acting on a test particle. But in practice, all of the systems we see in the world around us are not like that: there's an unimaginable amount of atoms in the world around us. This course teaches you all about physics with many bodies. Similarly to Physics 5C, it starts off with methods used to count the distribution of energy states within the system under various conditions and derives the principles of thermodynamics from them, but goes into greater depth and detail, doing everything from defining temperature and entropy to deriving the specific heat of solids and modeling how heat engines work. The material in this course has applications to astrophysics, condensed matter, biophysics, and other fields.

*Prior to taking this class, completion of 5C/7C is strongly recommended.*

As a first pass at introductory quantum mechanics for most students, Physics 137A is a truly mind-blowing course which reveals the fundamental weirdness governing the universe. One can expect to learn quantum mechanics through its various formulations to describe the ever elusive “wavefunction,” which governs the inherently probabilistic dynamics of quantum systems. Using the all-important Schrödinger equation, Physics 137A explores what happens to particles in free space, infinite wells, and quadratic “harmonic oscillator” potentials, among others. The class uses lessons from these toy models to derive the level scheme of the hydrogen atom from basic principles. In addition, the class explores the uncanny valley produced by the at-once intuitive and elusive concept of spin, a discussion which yields to an example of quantum entanglement.

*Prior to taking this class, completion of 5C/7C is strongly recommended.*

Whereas Physics 137A discusses fundamental postulates of quantum mechanics and simple toy models, Physics 137B equips the connoisseur of “real physics” with the ability to handle real systems with clever tools. After picking up inventive approximate methods such as perturbation theory (for small changes to a potential), the variational principle (for estimating energies of intractable systems), and WKB theory (for slowly varying potentials in certain regimes), students will be able to handle systems as diverse and practical as the helium atom, atomic level transitions, and nuclear decay. The class also addresses identical particles as well as scattering, increasing the class’ portfolio of useful lessons. Depending on the instructor, this class may also provide an introduction to quantum information or other special topics.

*Prerequisite is 137A.*

## Upper Division Course Electives

Physics 110B is an extension of the required Physics 110A that demonstrates how to apply the basic principles of Electromagnetism in practical and theoretically interesting settings. Although specific topics and course layout vary from instructor to instructor, the course often starts by formulating electromagnetism relativistically which often makes the theory more amenable to Green's function approaches (which prove invaluable for actually solving electromagnetic problems). Subsequently, the course explores the physics of moving charges which naturally leads to the modern theory of light. With this, in hand, topics such as wave propagation in media, radiation, Fourier optics, interference and diffraction, ray optics, etc. can all be dealt with very systematically.

A thrilling elective, Physics 129 provides the framework for thinking about high-energy physics. After tackling relativistic formulations of quantum mechanics, Physics 129 quickly dives into a first-pass at the bizarre intricacies of quantum field theory, uncovering, along the way, the mathematical origin of spins, antiparticles, and the fundamental forces. The class caps off with a candid mathematical sketch of the sensationalized, mass-giving Higgs mechanism and a description of the standard model. Depending on the dispositions of the instructor, Physics 129 can either take an extremely theoretical focus or emphasize experimental considerations and data analysis.

Physics 138 is an elective that teaches techniques from the exciting world of Atomic, Molecular, and Optical (AMO) physics. Although specific topics and course layout vary from instructor to instructor, the course broadly explores the interaction between light and atoms/atom-like objects in experimentally relevant settings.

From a theoretical standpoint, this course teaches some pen-and-paper techniques for understanding the quantum dynamics of atoms/atom-like objects. The intuition gained from this portion of the course helps one understand more complex systems wherein there are many interacting degrees of freedom. Furthermore, the course teaches the theory of open quantum systems (i.e. quantum systems (say an atom) that are coupled to the environment). This is crucial for understanding how quantum effects manifest in experiments (wherein one is always coupled to the experimental environment).

From an experimental perspective, this course teaches the organizing principles necessary to understand modern AMO experiments. Namely, the theory of laser cooling, saturation spectroscopy, quantum state preparation, etc. are all explored in depth. Often times, the course also features guest lectures from specialists in the faculty about trapped-ion experiments, Bose-Einstein Condensates, Nitrogen-Vacancy centers, precision measurements, and much more!

Physics 139 brings us face-to-face with Einstein's General Theory of Relativity which forms our current understanding of (low-energy) gravity. Although specific topics and course layout vary from instructor to instructor, the course broadly starts by presenting some experimental motivations for special relativity (while also reviewing the subject). Subsequently, the course teaches how special relativity can naturally be put in the language of Differential Geometry (which describes roughly how one does calculus on arbitrary surfaces). Finally, after going through some experimental motivations and organizing principles of general relativity, the course presents the theory in its full mathematical formalism. Finally, solutions to Einstein's theory of General Relativity are presented including black hole solutions, low-mass solutions (in a linearized approximation), etc!

Physics 141A describes the exciting physics that emerges in crystals, periodic lattices made of atoms that contain both bound and free electrons. Broadly speaking, the course seeks to understand how electrons behave in lattices and interact with the dynamics of the lattice.

From a theoretical perspective, one gets their first taste at many-particle quantum physics. This is done by neglecting interactions between electrons and reducing the many-particle problem to a single-particle problem. Although single-particle physics seems to be the subject of 137A/B, fret not, solving the single-particle problem for interesting and experimentally relevant potential landscapes proves to be quite the task!

From an experimental perspective, this class aids in understanding about real materials and the origin of conductors, insulators, semi-conductors, etc. Truly, this class teaches the basic language used by condensed matter experimentalists daily!

Physics 141B continues the exploration of materials physics by exploring how magnetism, ferroelectricity, superconductivity, and the like arises in materials. Really, this course takes the language learned in 141A and starts to apply it in some highly non-trivial settings!

The topic of this class varies from semester to semester and generally covers a relatively specialized field, often one in which the instructor has specific expertise. Physics 151 topics are generally disclosed and advertised before the semester starts. The rapidly changing focus of the class means that students should expect to be more flexible with regard to impromptu deviations from the syllabus, though its specific dives into interesting subjects often make it a very rewarding experience.

**Physics C161**

This class covers the fundamentals of cosmological physics. The class begins with a brief overview of general relativity and elaborately explores topics such as the Friedmann-Robertson-Walker metric, big bang nucleosynthesis, inflation, and large scale structure. Astronomy C161 is for the student seeking an introduction to the field centered around answering deep questions about the birth and evolution of the universe.

**Physics 177**

Physics 177 is a physical biology survey course. Building upon a basic knowledge of chemistry and biology, students use concepts learned from electromagnetism and statistical mechanics to approach biophysical problems. Physics 112 (Statistical Mechanics) is recommended as a prerequisite. The course is a good way to get a taste of biophysics, as it briefly touches upon important concepts within the field such as chemical kinetics, diffusion, and gene expression. However, the structure and focus of each semester are highly dependent on the professor’s own unique interests.

**Physics 188**
This class covers many topics in data science and computational techniques that are useful in physics, from doing calculus on a computer, topics in linear algebra, optimization, statistical analysis, and even machine learning and neural nets. It begins with and often uses the Bayesian interpretation of statistics and probability, which unlike the frequentist approach to probability and statistics that you (probably) worked with in high school and lower division, sees the two as subjective measures that are updated with each new result. This course expands on and goes beyond the data analysis topics covered in Physics 77 and 5BL-5CL, approaching it from a new perspective, and is really useful if you do a lot of data analysis or computational stuff in your research. Keep in mind, though, that the lectures cover a lot of material in little time (though the assignments are typically manageable).

**Physics C191**
This class is all about the fascinating new field of quantum computing. It starts with an introduction to the basics of quantum mechanics, but then delves into translating the measurement and system-transformation operators into a circuit operating on quantum information, quantum algorithms (including the one that can crack most modern-day encryptions), and lastly, corrections for errors common in quantum computing. The course ends with a final group project that includes a presentation and a written deliverable. It is a really interesting class about a very promising field and I'd strongly recommend it.