# Applied Physics Courses

**For more information on specific courses, including prerequisites, registration details and any last-minute changes, visit my.harvard**

## Physics as a Foundation for Science and Engineering, Part I

AP 50a is the first half of a one-year, team-based and project-based introduction to physics. This course teaches scientific reasoning and problem-solving skills. You will work in teams on three, month-long projects, each culminating in a project fair. The twice-weekly class periods are all inclusive: there are no separate labs or discussion sections, but you must set attend a 75-minute section on Thursday or Friday to work on your projects with your team in the teaching labs (w. AP50a topics include: kinematics, Newton's Laws, conservation laws, angular dynamics, and simple harmonic motion.Course Note: AP50a is designed specifically for engineering and physics majors and is equivalent in content and rigor to a standard introductory physics course for scientists and engineers such as Physics 15a, but focuses on the application of physics to real-world problems.

## Physics as a Foundation for Science and Engineering, Part II

AP 50b is the second half of a one-year, team-based and project-based introduction to physics. This course teaches students to develop scientific reasoning and problem-solving skills. AP50b topics include: electrostatics; electric currents; magnetostatics; electromagnetic induction; Maxwell's Equations; electromagnetic radiation; geometric optics; and, wave optics. Multivariable and vector calculus is introduced and used extensively in the course. Students work in teams on three, month-long projects, each culminating in a project fair. The twice-weekly class periods are all inclusive: there are no separate labs or discussion sections.

## Introduction to Solid State Physics

The physics of crystalline solids and their electric, magnetic, optical, and thermal properties. Designed as a first course in solid-state physics. Topics: free electron model; Drude model; the physics of crystal binding; crystal structure and vibration (phonons); electrons in solids (Bloch theorem) and electronic band structures; metals and insulators; semiconductors (and their applications in pn junctions and transistors); plasmonic excitations and screening; optical transitions; solid-state lasers; magnetism, spin waves, magnetic resonance, and spin-based devices; dielectrics and ferroelectrics; superconductivity, Josephson junctions, and superconducting circuits; electronic transport in low-dimensional systems, quantum Hall effect, and resonant tunneling devices.

## Mechanics in Earth and Environmental Science

Introduction to the mechanics of fluids and solids, organized around earth and environmental phenomena. Conservation laws, stress, deformation and flow. Inviscid fluids and ocean gravity waves; Coriolis dominated large scale flows. Viscosity and groundwater seepage; convective cells; boundary layers. Turbulent stream flows; flood surges; sediment transport. Elasticity and seismic waves. Pore fluid interactions with deformation and failure of earth materials, as in poro-mechanics of consolidation, cracking, faulting, and landslides. Ice sheets and glacial flow mechanics.

## Quantum and Classical Electromagnetic Interaction with Matter

The first half of the course will cover the interaction of quantized atoms with electromagnetic fields, introducing a number of basic concepts such as coherent Rabi transitions vs. rate-equation dynamics, stimulated & spontaneous transitions, and energy & phase relaxations. These will be then used to study a range of applications of atom-field interactions, such as nuclear magnetic resonance, molecular beam and paramagnetic masers, passive and active atomic clocks, dynamic nuclear polarization, pulse sequence techniques to coherently manipulate atomic quantum states, and laser oscillators with applications. We will also touch upon the interaction of quantized atoms with quantized fields, discussing the atom + photon (Jaynes-Cummings) Hamiltonian, dressed states, and cavity quantum electrodynamics. The second half will cover the classical interaction of electromagnetic fields with matter, with special attentions to collective electrodynamics in particular, magnetohydrodynamics and plasma physics with applications in astrophysics, space physics, and Bloch electrons in crystalline solids.

## Electrical, Optical, and Magnetic Properties of Materials

This course covers the electrical, optical and magnetic properties of technologically important materials systems. It provides a quantitative description of structure-property relations by introducing tensor properties, crystal symmetry, Neumann's principle and Curie principle. A variety of properties of materials are then introduced, including pyroelectricity, dielectricity, piezoelectricity, ferroelectricity; pyromagnetism, magnetoelectricity, piezomagnetism, ferromagnetism; defect chemistry, transport properties and applications in semiconducting, dielectric and energy storage materials; crystal optics including birefringence, Pockels effect, Kerr effect, photoelastic effect and optical activity. Ferroelectric, ferromagnetic and topological phase transitions are also covered as special topics.

## Landmark Papers in Soft Matter

A seminar course that will survey classical, landmark, papers in soft matter physics with a slight bias towards experimental works.

## Chemistry in Materials Science and Engineering

Select topics in materials chemistry, focusing on chemical bonds, crystal chemistry, organic and polymeric materials, hybrid materials, surfaces and interfaces, self-assembly, electrochemistry, biomaterials, and bio-inspired materials synthesis.

## Computational Design of Materials

This course covers theoretical background and practical applications of modern computational atomistic methods used to understand and design properties of advanced functional materials. Topics include interatomic potentials and quantum first-principles energy models, wave function and density functional theory methods, Monte Carlo sampling and molecular dynamics simulations of phase transitions and free energies, fluctuations and transport properties, and machine learning approaches. Methods are applied to study microscopic and quantum-level effects in materials for energy conversion and storage, molecules, soft materials, electronic devices, and low-dimensional materials.

## Computational Physics of Solids and Fields

Description coming soon.

## Solids: Structure and Defects

Bonding, crystallography, diffraction, phase diagrams, microstructure, point defects, dislocations, and grain boundaries.

## Statistical Mechanics

Basic principles of statistical physics and thermodynamics, with applications including: the equilibrium properties of classical and quantum gases; phase diagrams, phase transitions and critical phenomena, as illustrated by the liquid-gas transition and simple magnetic models. Time permitting, introduction to Langevin dynamics and polymer physics.

## Inference, Information Theory, Learning and Statistical Mechanics

We will build introduce modern applications of Statistical Mechanics from information theory, to coding and compression, finding probabilistic answers to poorly posed inverse problems to unsupervised learning. Further we will study supervised learning and machine learning. All of these topics will be taught using examples in the primary literature with an emphasis on the applications of the tools and framework we develop in the course. Applications will be taught through problems in genomics, neuroscience, mechanics, geophysics and engineering.

## Electron Microscopy Laboratory

Lectures and laboratory instruction on transmission electron microscopy (TEM) and Cs corrected, aberration-correction microscopy and microanalysis. Lab classes include; diffraction, dark field imaging, X-ray spectroscopy, electron energy-loss spectroscopy, atomic imaging, materials sample preparation, polymers, and biological samples.

## Introduction to Quantum Theory of Solids

Electrical, optical, thermal, magnetic, and mechanical properties of solids will be treated based on an atomic scale picture and using the independent electron approximation. Metals, semiconductors, and insulators will be covered, with possible special topics such as superconductivity.

## Quantum Theory of Solids

This course presents theoretical description of solids focusing on the effects of interactions between electrons. Topics include Fermi liquid theory, dielectric response and RPA approximation, ferro and antiferromagnetism, RKKY interactions and Kondo effect, electron-phonon interactions and superconductivity.

## Mesoscale and Low Dimensional Devices

Concepts of condensed matter physics are applied to the science and technology of beyond-CMOS devices, in particular, mesoscale, low-dimensional, and superconducting devices. Topics include: quantum dots/wires/wells and two-dimensional (2D) materials; optoelectronics with confined electrons; conductance quantization, Landauer-Buttiker formalism, and resonant tunneling; magneto oscillation; integer and fractional quantum Hall effects; Berry phase and topology in condensed matter physics; various Hall effects (anomalous, spin, valley, etc.); Weyl semimetal; topological insulator; spintronic devices and circuits; collective electron behaviors in low dimensions and applications; Cooper-pair boxes and superconducting quantum circuits.

## Special Topics in Applied Physics

Supervision of experimental or theoretical research on acceptable applied physics problems and supervision of reading on topics not covered by regular courses of instruction.

## Special Topics in Applied Physics

Supervision of experimental or theoretical research on acceptable applied physics problems and supervision of reading on topics not covered by regular courses of instruction.