PhD Programs in Mathematical Physics

Students interested in the field of physics can pursue a PhD in Mathematical Physics. Learn more about these programs including possible courses, admission requirements, and possible careers by reading further.

How to Earn a PhD in Mathematical Physics

Individuals who want to earn a PhD degree in mathematical physics will need to meet program admission requirements, such as holding a 3.0 GPA in all prior coursework, completing the GRE exam, submitting letters of recommendation, and writing a statement of purpose before they can start their academic journey. This program will typically take a minimum of four years to complete, and some of the courses that students can take over the course of their education include statistical mechanics, quantum mechanics, theoretical physics, and classical electrodynamics.

Statistical Mechanics

A course in statistical mechanics will introduce students to a variety of classical theories present in physics and about the development of new theories in the field. Other topics that can be covered in this class include equilibrium statistics, kinetic theories as they relate to liquids, thermodynamics, and equilibrium mechanics. Additionally, this course may also teach students about the Boltzmann equations and how to properly use them.

Quantum Mechanics

Quantum mechanics focuses on the topics of wave mechanics and the axioms of quantum mechanics. A class like this will introduce relativistic theory, and it may also cover a number of other areas like the hydrogen atom, the theory of angular momentum, and principles of matrix mechanics. Students can also get a better understanding of Schroedinger's wave mechanics and the Hilbert space methods.

Mathematical Physics

Students in a mathematical physics class can learn about matrix algebra, complex variables, linear vector spaces, and group theory. This course will teach students about the problems that may arise in the field of mathematical physics, and how to handle them. Other areas that could be covered include integration methods and the unbound operators in Hilbert space.

Classical Electrodynamics

Students are introduced to the field of advanced electromagnetostatistics and time-varying fields. Other topics that can be covered here include electrostatistics, conservation laws, radiation theory, and physical optics. By the conclusion of this course, students will be familiar with Maxwell's equation and Green's functions.

Nuclear Physics

A course in nuclear physics can touch on current research being done in the field, in addition to covering hadronic physics and nuclear astrophysics. Students will learn about the processes of nuclear reactions and understand nuclear structures.

Related Careers

Physicist or Astronomer

Physicists and astronomers study the interactions of matter and energy, and they can work in settings like offices, laboratories, or observatories. These professionals might design experiments and scientific equipment and analyze physical or mathematical data. Physicists and astronomers made $119,580 per year, in May 2018, according to data provided by the US Bureau of Labor Statistics (BLS), and there is expected to be job growth of 9% from 2018-2028, which is faster than average. Those with a PhD in Mathematical Physics will be well prepared for this position due to their extensive knowledge of math, advanced and specialized physics topics, and electrodynamics.

Postsecondary Teacher

After earning a Mathematical Physics PhD, students can obtain positions as physics professors at colleges or universities due to their extensive training in research on specialized topics in math and physics. Postsecondary teachers typically need to have a PhD in their field, and these teachers had a median salary of $78,470 as of 2018, according to the BLS. The expected employment growth rate from 2018 to 2028 is 11%, which is faster than the average.


Another position that those with a Mathematical Physics PhD can pursue is as a mathematician, and these professions had a median 2018 salary of $92,030 based on BLS data. Mathematicians are responsible for using data and math to solve problems, and they typically need to hold an advanced degree in a field of mathematics. The expected growth rate over the 10 year period from 2018 to 2028 is 30%, which is significantly faster than average.

Job TitleMedian Salary (2018)*Job Outlook (2018-2028)*
Physicist or Astronomer$119,5809%
Postsecondary Teacher$78,47011%

*Source: U.S. Bureau of Labor Statistics

Students that want to earn a PhD in Mathematical Physics will spend a minimum of four years enrolled in the program, and they may take courses like nuclear physics, mathematical physics, classical electrodynamics, statistical mechanics, and more. Once they earn their degree, students can move on to obtain careers as postsecondary teachers, mathematicians, physicists or astronomers.