Physics and Astronomy

The M.A. and M.S. Degrees
Ph.D. Degree Requirements
The Ph.D. Degree in Physics with Astrophysics Option
The Ph.D. Degree in Physics with Business Option
Courses of Instruction

Available on the Master of Arts, Master of Science and Doctor of Philosophy degrees.

Prerequisites:
B.A. or B.S. with a physics major, or 24-semester-hour equivalent including intermediate or advanced undergraduate courses in mechanics, electricity and magnetism, atomic and nuclear or modern physics or their equivalents. Twelve semester hours must be of junior or senior level. Required are mathematics through differential equations and a course in general chemistry. Prerequisites to a graduate minor in physics are 20 hours of physics including advanced courses in mechanics, electricity and magnetism, and modern physics or their equivalents.

Students deficient in any area of preparation may be required to take the necessary course work during the first year of graduate study. Scores on the Graduate Record Examinations are used as an aid in the overall evaluation of the applicant's graduate potential.

The M.A. and M.S. Degrees


The M.A. degree requires 30 approved semester hours of graduate courses with a minimum of 18 semester hours in Physics and a knowledge of one foreign language. A thesis and a minor are optional. An oral exam over course work and thesis, if any, is required.

The M.S. degree requires 30 approved semester hours with a thesis or 36 semester hours without a thesis. Course requirements for the degree are: Physics 60303, 60313, three from Physics 60203, 60403, 60413, 60503 and 60603, plus a minimum of 6 additional semester hours in Physics. There is no foreign language requirement. An oral exam over course work and thesis, if any, is required.

Ph.D. Degree Requirements


1. Course work.
Completion of the following courses with an average grade of B or better:
Physics 60303, 60313 Quantum Mechanics
Plus four from the following:
Physics 60203, Classical Mechanics;
Physics 60403, 60413, Electrodynamics;
Physics 60503, Solid State Physics;
Physics 60603, Statistical Physics
A minimum of nine hours of Physics 60970 Research Problems must be completed with an average grade of B or better.

Additional course work may be required to ensure adequate preparation for the specified courses. Each full-time student is required to participate in graduate seminars.

The course requirements for any course other than Physics 60970, Research Problems, may also be met by satisfactory performance on a written examination administered by the faculty over the subject matter of that course, or by transfer of credit in an equivalent course from another institution.

There is no language requirement for the Ph.D. degree.

2. Pre-dissertation qualifying exam.
This exam, which is normally taken during the fourth semester of graduate study, consists of three parts:

a. an acceptable written report concerning either research completed at TCU or a proposal for the dissertation research including a description of any research already completed. The written report must be submitted to the graduate faculty of the department at least two weeks prior to the oral exam. Details on the required format for the report are available from the department.
b. an oral presentation at a physics and astronomy department colloquium, usually on the subject of the written report. a comprehensive oral exam administered by the graduate faculty of the department to assess a student's preparation in basic physics and readiness to carry out the dissertation research. If the graduate faculty of the department attach a condition to passing the predissertation exam, (e.g. revision of the predissertation report or submission of additional material), the additional work must be completed by a specified deadline. The removal of the condition is subject to the approval of the graduate faculty.

The predissertation qualifying exam, in whole or in part, may be repeated once. Students who do not pass the exam are encouraged to complete the requirements for a Master's degree if they have not already done so.

Completion of the above course requirements and the predissertation qualifying exam constitute admission to candidacy for the Ph.D. degree.

3. Dissertation.
Completion of a dissertation consisting of an original research project directed by a faculty member at TCU. Six hours of 90980 Dissertation and six hours of 90990 Dissertation are required. A final oral exam in defense of the dissertation is required and a paper based on the dissertation research must be submitted for publication in an appropriate scientific journal.
Each full-time graduate student pursuing a degree in physics is required to participate in the undergraduate teaching function of the department. This requirement is met by assisting in undergraduate labs, giving laboratory instructions, grading papers, conducting problem sessions or offering tutorial help. The assignment varies depending on the interest and experience of the student and the degree of involvement in thesis or dissertation research, and usually amounts to 10 hours per week or less.

The Ph.D. Degree in Physics with Astrophysics Option


The Ph.D. in Physics is also available with an Astrophysics option.

Course Work.
Completion of the following courses with an average grade of B or better:
Physics 60743, Astrophysics
Physics 60303 Quantum Mechanics
Physics 60403, Electrodynamics
Plus three from the following:
Physics 60203, Classical Mechanics
Physics 60313, Quantum Mechanics
Physics 60413, Electrodynamics
Physics 60603, Statistical Physics
A minimum of nine hours of Physics 60870, Research Problems in Astronomy, must be completed with an average grade of B or better. Students in the Astrophysics option may also be required to take Physics 70743, Advanced Topics in Astrophysics, to ensure an adequate background for their dissertation research.

Except for the courses specified above, the remaining regulations concerning course work, pre-dissertation qualifying exam, and dissertation are the same as those prescribed above for the Ph.D. in Physics.

The Ph.D. Degree in Physics with Business Option


The Ph.D. in Physics is also available with a Business option. Students entering the Ph.D. program with a B.S. degree are normally expected to complete the Ph.D. requirements within five years. At the end of the fourth year of graduate studies, a candidate for the Ph.D. degree in Physics who has demonstrated sufficient progress in research (dissertation), may submit a written request to the Department of Physics for admission to this program. Providing there is a clear indication that the student can reasonably be expected to complete all the requirements for the Ph.D. within five years, permission will be granted to apply to the Director of Admissions of the MBA Program of the Neeley School of Business. During the fifth year the student is expected to continue with the dissertation on a reduced scale, and, if on Departmental Teaching Assistantship, to perform designated departmental teaching duties. Students entering the Ph.D. program with advanced standing (M.S. degree or more) can request an accelerated program.

In addition to the course work, qualifying examinations, and dissertation requirements specified for the Ph.D. degree in Physics, the student will satisfy the following conditions specified by the School of Business:
1. Students electing to take the Business Option will take the 18 hours of MBA coursework over the course of two consecutive semesters (entering in the Fall and finishing in the Spring semesters).
2. Students are required to attend the START Workshop conducted by the School of Business that occurs just before the start of the fall semester. Students are assessed a fee for the workshop.
3. The School of Business will accept the results of the GRE.
4. The Director of Admissions has sole authority to admit physics Ph.D. candidates to the MBA program (whether they seek the MBA degree or the Option).
5. Under the assumption that the students come to the program with a good background in Statistics, they would take the following courses:

a. Fall Semester

1. Corporate Financial Reports
2. Interpreting Financial Reports
3. Business Strategy and Structure
4. Managing People

b. Spring Semester

1. Management of Financial Resources
2. Market Driven Strategy
3. Managing Information Technology

6. The foregoing may be adjusted in the event of a realignment in the sequence of courses in the MBA program.
7. Students who wish to continue their studies in the program after their first year of business courses and pursue the MBA degree:

a. Will, with the approval of the Director of the MBA Program, be permitted to transfer in for credit a total of six hours of 60000 or 70000 level graduate physics course work. Transfer will be approved for: 1. A graduate level course that is equivalent to DESC (Statistics) and 2. Other 60000 or 70000 level course work taken in the Physics Department.

b. Will be required to complete such additional coursework as required of other MBA students and as is provided in the applicable TCU Graduate Studies Bulletin. The student will work closely with the Academic Program Director to plan his/her schedule.

c. Will be required to attend (in the second year of the MBA program) four of the Industry-Led Perspective Series seminars. This series brings corporate executives to speak on some issues relevant to business. A student could satisfy this requirement the first year.

Prospective candidates for the Ph.D. Degree in Physics or the Ph.D. with Business Option should be advised that the maximum term of fellowship or assistantship support through the Department of Physics is five years, and support for MBA courses from the TCU Physics Department fellowships or assistantship is limited to 18 hours. Financial support for additional hours required for completion of the MBA degree would be the student's responsibility; students would be eligible to apply for financial aid for the second year of MBA study from the Neeley School of Business.

The following is a complete list of courses offered by this department. Go to Class Searchon the Registrar's Page to see which courses are being taught this semester.

Courses of Instruction

The following courses are offered for seniors and graduate students when there is sufficient interest.

50030 SEMINAR IN CONTEMPORARY PHYSICS. Prerequisite: Permission of instructor. Students enrolled will be expected to participate in, prepare and lead discussions on selected topics in physics as suggested by the current journal literature.

50703 NONLINEAR DYNAMICS. Prerequisites: Permission of instructor. Physics 30553 is recommended. Characterization of chaos, routes to chaos, dissipative dynamical systems, Hamiltonian systems.

50713 CONTEMPORARY TOPICS IN PHYSICS. Prerequisite: Departmental permission. Regularly scheduled course on subjects of interest to students and faculty. Possible topics may include but are not limited to: Atomic and molecular physics, Atom optics, Biophysics, Mathematical physics and High-energy nuclear physics.

50723 INTRODUCTION TO SOLID STATE PHYSICS. Prerequisite: Physics 30493; Math 30524. Crystal structure, lattice dynamics, free electron theory, band theory, optical, electric and magnetic properties of solids.

50733 COMPUTATIONAL PHYSICS. Prerequisite: Physics 20483 and Math 30524. Computational methods used in physics, systems of linear equations, eigenvalue problems, numerical solution of differential equations using different computing environments.

50743 ASTROPHYSICS. Prerequisite: Departmental permission.. The distance scale, applications of dynamics, statistical mechanics, relativity and quantum theory to astrophysical phenomena, theory of stellar structure, processes in the interstellar medium and selected topics in cosmology.

50970 SPECIAL PROBLEMS IN PHYSICS. Prerequisite: Departmental Permission. Advanced work in physics, whose nature is to be determined by the previous preparation and interest of the individual. Credit will depend upon the nature of the study and the amount of work taken.

The following courses are offered regularly.


60203 CLASSICAL MECHANICS.
Prerequisites: Physics 30553 or equivalent. Variational principles and Lagrange equations, rigid body motion, Hamiltonian mechanics, canonical transformation, Lagrange and Poisson brackets, Hamilton- Jacobi theory, continuous systems and fields.

60303 QUANTUM MECHANICS.
Prerequisite: Physics 40113 or equivalent. Foundations of quantum mechanics, with applications to atomic and nuclear physics.

60313 QUANTUM MECHANICS.
Prerequisite: Physics 60303. Continuation of 60303.

60403 ELECTRODYNAMICS.
Prerequisite: Physics 40653 or equivalent. Electrostatic and magnetostatic fields. Time-dependent electromagnetic phenomena. Maxwell's equations and general electrodynamic theorems derivable therefrom. Electromagnetic radiation. Covariant formulation of the electromagnetic field equations.

60413 ELECTRODYNAMICS.
Prerequisite: Physics 60403 or permission of instructor. This is a second part of the two semester course. It includes electromagnetic radiation, coherent optics, diffraction, Fourier optics, wave guides, lasers and discussion of non-linear phenomena.

60503 SOLID STATE PHYSICS.
Prerequisite: Physics 60303, 60313 and 50723 or equivalent. Symmetry and crystal structure, ionic and covalent bonds, metals, band theory, thermal and optical effects in solids, and selected topics on magnetic properties, superconductivity and surface science.

60603 STATISTICAL PHYSICS.
Prerequisite: Physics 30603 or equivalent and Physics 60203, 60313. General principles, kinetic theory, partition functions, Bosons and Fermions, linked cluster expansions, distribution functions, Brownian motion.

60743 ASTROPHYSICS.
Prerequisite: Departmental Permission. Origin and interpretation of stellar spectra. Energy generation and transport, nucleosynthesis. Stellar structure and stellar evolution. Interstellar medium, nebulae. Galaxies. Cosmology.

60870 RESEARCH PROBLEMS IN ASTRONOMY.
Prerequisite: Departmental Permission. Directed research in the follow areas:
Observational astronomy
Galaxy structure and evolution
Stellar populations
Large-scale structure

60960 PHYSICS SEMINAR.
Prerequisite: Graduate standing in Physics or approval of instructor. Participation in graduate colloquium and occasional presentation of appropriate topics to graduate faculty.

60970 RESEARCH PROBLEMS.
Directed research in the following areas:
Atom optics
Electron-atom collisions
Molecular and solid state physics
Statistical physics
Positron annihilation spectroscopy

70771.
Selected when enrolling only for non-thesis examination or preparation for the examination.

70980 THESIS.
Prerequisite: Permission of Chair of Department.

70990 THESIS.
Prerequisite: Admission to candidacy.

80090 THE TEACHING OF PHYSICS AT THE COLLEGE LEVEL.
Prerequisite: Graduate standing in physics and approval of instructor. Supervised preparation and delivery of lectures and demonstrations, and preparation and evaluation of examinations.

90970 RESEARCH PROBLEMS IN PHYSICS.
Prerequisite: Graduate standing and departmental permission.

90980 DISSERTATION.
Prerequisite: Permission of Chair of Department.

90990 DISSERTATION.
Prerequisite: Admission to candidacy. Continuation of 90980. A minimum of 12 hours of dissertation is required.

The following courses are offered for advanced graduate students when the demand develops.


60120 MATHEMATICAL METHODS OF PHYSICS.
Prerequisite: Departmental approval. Selected topics in mathematical physics.

70133 ATOMIC COLLISION PHYSICS.
Prerequisite: Physics 60303 and 60313. Theoretical, computational and experimental techniques used in electron, photon, atomic and molecular collision physics.

70203 NUCLEAR AND PARTICLE PHYSICS.
Prerequisite: Physics 60313. Nuclear and particle classifications and properties; nuclear two-body problem; nuclear models; passage of radiation through matter; detection methods and accelerators; nuclear and particle spectroscopy; gamma decay, beta decay and the weak interactions, Kaons, particle resonances; nuclear reactions; experiments at high energy.

70303 ADVANCED QUANTUM MECHANICS.
Prerequisite: Physics 60313. An introduction to the relativistic Dirac theory of the electron and to the non- relativistic quantum mechanical many- body problem.

70413 STATISTICAL PHYSICS.
Prerequisite: Physics 70403. Lattice statistics, critical phenomena, propagators and methods for distribution functions, transport phenomena and irreversibility, second quantization and Green's functions.

70503 MOLECULAR PHYSICS.
Prerequisite: Graduate standing in physics or approval of instructor. Electronic, vibrational and rotational spectroscopy of polyatomic molecules. Applications of group theory to molecular spectra and structure. Fourier transform laser, electron paramagnetic resonance and other spectroscopic techniques.

70703 CHEMICAL PHYSICS.
Prerequisite: Physics 60303. Quantum Chemistry, structure of molecules and intermolecular forces, molecular relaxation processes, light scattering, nonlinear optical methods, molecular beams, NMR and other experimental techniques.

70743 ADVANCED TOPICS IN ASTROPHYSICS.
Prerequisite: Physics 60870 or Departmental Permission. Regularly scheduled course on advanced topics in astronomy and astrophysics, including the following:
Stellar Atmospheres: Basic methods and applications of radiative transfer. Theory and interpretation of astronomical spectra: line profiles, LTE and non-LTE line formation, abundances, model atmospheres, curve-of-growth.
Stellar Interiors: Solution of the equations of stellar structure, analytic approximations and theory relating to equilibrium stellar models, nucleosynthesis in massive stars, final phases of stellar evolution.
Galactic Structure: The interstellar medium, galaxy kinematics, interacting galaxies, evolution and classification of galaxies, extragalactic radio sources, quasars, cosmological models.

70803 THEORETICAL ATOMIC AND MOLECULAR PHYSICS.
Prerequisite: Physics 60303 and 60313. Theoretical study of electronic structure and molecular vibrations and rotation, Hartree-Fock and Many Body Perturbation Theory. Computer calculation of electronic structure.

70903 QUANTUM OPTICS.
Prerequisite: Physics 60203 and 60213. Study of Laser Physics, interaction of light and matter, nonlinear phenomena and quantum nature of light.

90960 SEMINAR IN THEORETICAL PHYSICS.
Prerequisites: Graduate standing and approval of instructor.