New graduate students arrive with a wide range of Physics and Physics-related course background experiences. For this reason, the Department asks all new students to complete a set of four assessment exams, described below, in order to provide a snapshot of each student's knowledge and experience with core material. Exam results are used to advise students on appropriate course selection at Duke and also to help students self-assess specific areas of course material background that may deserve attention going forward. The exams are typically given just prior to orientation activities that occur in the two weeks before the Fall semester commences. For the 2020-21 academic year, the exams will be given on-line and will be available to take during a time window of several days in early August. The four exams cover topics from classical mechanics, electricity and magnetism, thermal dynamics and quantum mechanics, at the intermediate/advanced undergraduate level. Each exam is timed with a duration of approximately two hours.

### Content and Format

In the period just prior to the Fall semester, entering graduate students take a series of four assessment exams that provide a helpful measure of the student's knowledge in Classical Mechanics, Classical Electromagnetism, Thermal Physics and Quantum Mechanics, at the intermediate/advanced undergraduate level. Typical exam format consists of several short answer questions followed by two or three more substantial problems. Material covered in each exam includes:

**Classical Mechanics **- topics include Newtonian mechanics, conservation laws, oscillations, Langrangian and Hamiltonian methods, systems of particles, rigid body dynamics, nonlinear systems and coupled oscillations. The content and level of problems are similar to those found in the textbook Marion and Thornton, *Classical Dynamics of Particles* *and Systems,* 5th edition.

**Classical Electromagnetism **- topics include electrostatics, magnetostatics, dielectric and magnetic material, boundary value problems, multipoles, electromagnetic induction, Maxwell's equations, conservation laws, electromagnetic waves, radiation, electrodynamics and relativity. The content and level of problems are similar to those found in the textbook by Griffiths, *Introduction to Electrodynamics*, 4th edition.

**Thermal Physics** - topics include the laws of thermodynamics, entropy, heat engines, free energies, chemical potential, classical ideal gases, phase transitions and phase diagrams, Boltzmann statistics, partition function, quantum ideal gases (Fermi and Bose cases), Einstein and Debye models, thermal radiation and kinetic theory. The content and level of problems are similar to the found in the textbook by Schroeder, *An Introduction to Thermal Physics*, 2nd edition.

**Quantum Mechanics** - topics include the wave function, Schrödinger wave equation, state vector, Dirac notation, Hilbert space, operators, uncertainty principle, one-dimensional quantum problems (e.g. tunneling and harmonic oscillator), three-dimensional quantum problems (e.g. ideal Hydrogen atom), angular momentum operators, spin, angular momentum addition and Clebsch-Gordan coefficients, time-independent perturbation theory, fine and hyperfine structure of Hydrogen, identical particles and multielectron atoms and elementary scattering theory. The content and level of problems are similar to those found in the textbook by Griffiths and Schroeter, *Introduction to* *Quantum Mechanics*, 3rd edition.

### Purpose

The purpose of the exams is to assess the preparedness of the student to take each of the core graduate level courses. Assessment exam results serve as a springboard for discussion with the Director of Graduate Studies (DGS) regarding how to best structure the student's course schedule. For example, a student who does not perform optimally on an exam, may be advised to do background reading or take a preparatory graduate level course in the corresponding subject area prior to enrolling in the core graduate level course.

Instructors of the core graduate level courses may use the assessment exam results to determine the overall level of preparation by the students. This allows the instructor to better tailor the course to the students taking the course in any given year.

### Planning

To help provide an accurate snapshot of each student's preparation and background in the four core areas, it is recommended that students set aside preparation and review time during the weeks prior to the exams. Many students find it helpful to spend a few hours per day in the three to four weeks preceding the assessment exams reviewing related material from their undergraduate coursework. Specific examples of material that may be helpful to review from prior coursework include: textbook readings, old homework sets and exams and corresponding solution sets as well as lecture notes. In addition, it may be helpful to attempt to solve a few additional homework problems from the indicated or similar textbooks.