ODTÜ, Department of Physics.

Core Subjects and Reference Guide

Analytical Mechanics

Lagrangian and Hamiltonian formulation, constrained systems, symmeetries and conservation laws, variiational principle, canonical transformations and Hamilton-Jacobi theory, central force problem, rigid body motion, small oscillations.

Suggested Reference: H. Goldstein "Classical Mechanics"
Related Course: PHYS 502

Electromagnetic Theory (I, II)

Electrostatics, magnetostatics, Maxwell's Equations, plaıne electro- magnetic waves, radiation from moving charges, introduction to special relativity and the covariant formulation.

Suggested Reference: J. D. Jackson "Classical Electrodynamics"
Related Courses: PHYS 505, PHYS 506

Quantum Mechanics (I, II)

Quantum dynamics, angular momentum, tiime independent and time dependent approximation methods, identical particles and second quuantization, quantum theory of radiation, Dirac equation, scattering.

Suggested References: E. Merzbacher "Quantum Mechanics" J.J. Sakurai "Modern Quantum Mechanics" Bjorken-Drell "Relatiivistic Quantum Mechanics"
Related Courses: PHYS 507, PHYS 508

Methods of Mathematical Physics (I, II)

Functions of a compleex variable, speciial functions of mathematical physics, partial differential equations. Integral equations, series, calculus of variations, Green's functions.

Suggested References: George Arfken, "Mathematical Methods for Physicsts" Byron and Fuller, (vol, I, II) "Mathematics of Classical Quantum Mechanics" E. Butkov "Mathematical Physics"
Related Courses: PHYS 503, PHYS 504

Statistical Mechanics

Elements of the classical and quantum statistics, the partition function, ideal Fermi gas, ideal Bose gas, phase transitions.

Suggested References: K. Huang, "Statistical Mechanics" R.K. Pathria "Statistical Mechanics" F. Mandl, "Statistical Physics"
Related Course: PHYS 501

 

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The Department of Physics requires all Ph.D. candidates to pass a qualifying examination. Its purpose is to ensure that a student has sufficient general knowledge in physics to proceed successfully toward the Ph.D. degree.

The qualifying examination is a written examination administered in two evening sessions. Each session contains a problem on classical mechanics (including relativity), electricity and magnetism, quantum mechanics, and thermodynamics (statistical mechanics). The exam tests competence in material that will have been covered in a solid undergraduate degree course in physics, but with the depth of understanding and technical facility expected after one year's enrollment in a graduate program. Accordingly, the level is sometimes said to be intermediate between undergraduate and graduate. The material covered is as follows:

Classical mechanics at the intermediate level (Physics 326), plus the special theory of relativity. Typical texts are Marion, Symon, Becker, and Fowles.

Electricity and magnetism at the intermediate level (Physics 436), including boundary value problems. Typical texts are Lorrain, Corson and Lorrain, Reitz, Milford and Christy, and Nayfeh and Brussel, with mathematical competence expected at the level of Chapters 1 through 7 of Jackson, and the electromagnetism parts of Wyld. (Cables and waveguides may be covered on the exam, although not at the level of Chapter 8 in Jackson.)

Statistical physics at the intermediate level (Physics 427), including the use of the Boltzmann, Gibbs, Fermi-Dirac, and Bose-Einstein distributions, classical and ideal gases, and black-body radiation. Typical texts are Chapters 1 through 14 of Kittel and Kroemer and Chapters 1 through 13 of Reif. These ranges of chapters of chapters are suggested as a study guide; other topics may be covered on the exam, as shown in the example problems.

Quantum mechanics at the intermediate level (Physics 486,487) and the beginning graduate level (Physics 580). Typical graduate texts are Dicke and Witte, Gasiorowicz, Park, Merzbacher, Baym, Landau and Lifshitz, Sakurai, and Schiff. Typical undergraduate texts are Eisberg, Park, and Cassels.

The examination is constructed to test your knowledge of the fundamental principles in each subject, applied to situations of physical interest. Elaborate formal questions are avoided. In particular, the portion of the examination dealing with quantum mechanics covers simple applications of Schroedinger wave mechanics to both bound-state and scattering problems, few-level systems, the Pauli theory of electron spin, and perturbation theory.

Admitted graduates are strongly encouraged to prepare for the qualifying examination by working through past exams. These exams, which give the best indication of style. and content, are available on-line. Hard copies are on reserve in our library. More information is available in the Qual FAQ. You may also find the Physics Formulary or the NIST " Reference on Constants, Units, and Uncertainty" helpful.

When the Qual Exam is Offered

The written qualifying examination is given during the first or second week of the fall semester. Students entering the Ph.D program are required to take the qual by the beginning of their third semester that they are enrolled in the department, although they may elect to take it earlier. In the event of failure on the first try, a student is allowed one further attempt, which must be taken at the next offering. A "free shot" is available to all students at the time of their first enrollment. Failure on the free shot is not recorded and does not count against the student, but a pass is a bona fide pass. Thus, if you do some preparation, we encourage you to take the free shot; you have nothing to lose, and you may gain valuable insight into your own strengths and weaknesses to guide you in your selection of classes.

Some notes are allowed during the qual. You may bring one "pure math" integral table (e.g. CRC Handbook of Mathematical Formulae, or Gradshteyn and Ryzhik's Tables of Integrals, Series, and Products). You may not bring handbooks or textbooks containing physics formulae. Electronic calculators or slide rules may be used, but no other books, handwritten notes, laptop computers, or other aids are permitted in the examination room. A printed handout of traditional physics formulae will be supplied with the exam. In recent years, the overall pass rate on the qualifying examinations has been 80-90 percent.