2026 (Current Year) Faculty Courses School of Science Undergraduate major in Physics
Relativistic Quantum Mechanics
- Academic unit or major
- Undergraduate major in Physics
- Instructor(s)
- Daisuke Jido
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 1-2 Mon (M-103(H114)) / 1-2 Thu (M-103(H114))
- Class
- -
- Course Code
- PHY.Q331
- Number of credits
- 200
- Course offered
- 2026
- Offered quarter
- 2Q
- Syllabus updated
- Mar 23, 2026
- Language
- Japanese
Syllabus
Course overview and goals
In this course, relativistic quantum mechanics is discussed. After a review on special relativity is given, the Klein-Gordon equation is introduced as a relativistic generalization of the non-relativistic Schroedinger wave equation and its problems are discussed. Then the Dirac equation is introduced, which is the relativistic wave equation for an electron. Then applications of the Dirac equation, such as the plane wave solution, interaction with electromagnetic fields, Lorentz covariance, non-relativistic approximations, hydrogen atom spectrum and anti-particle are discussed.
Special relativity and quantum mechanics are the most important subjects in modern physics. Learning main ideas unifying these theories and how this unification leads to quantum theory of fields are very important in deeply understanding quantum mechanics and to catch up advanced subjects of modern physics such as elementary particle physics.
Course description and aims
You will be able to understand quantum mechanics describing relativistic phenomena, in particular, basics and applications of relativistic quantum mechanics of spin 1/2 particle based on the Dirac equation.
Keywords
Special relativity, Klein-Gordon equation, Dirac equation, antiparticle
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
Lectures by blackboard
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | special relativity and quantum mechanics |
Recall special relativity, Lorentz transformation and basics of quantum mechanics |
| Class 2 | Klein-Gordon equation |
Understand necessity of relativistic wave equation and the Klein-Gordon equation |
| Class 3 | Klein-Gordon equation: bound states in Coulomb force |
Learn bound states in Coulomb force as application |
| Class 4 | introduction of Dirac equation |
Understand that the Dirac equation consists of four components. |
| Class 5 | conservation current |
Derive the conserved current from the Dirac equation |
| Class 6 | solution of the Dirac equation for a free particle |
Understand how to find the plane wave solution to the Dirac equation |
| Class 7 | nonrelativistic limit and Tani-Foldy-Woutheuysen transformation |
Understand the non-relativistic approximation of the Dirac Hamiltonian |
| Class 8 | Lorentz covariance of the Dirac equation |
Understand the properties of the Dirac wave functions under the Lorentz transformations |
| Class 9 | Lorentz invariances and bilinear form |
Understand Lorentz invariant quantities and bilinear forms |
| Class 10 | solutions and their properties of the Dirac equation |
Understand the conserved quantities and the relation between spin and orbital angular momenta |
| Class 11 | interpretation of negative energy solution and Dirac's hole theory |
Understand antiparticles concluded by the Dirac equation |
| Class 12 | Dirac particles in spherical electrostatic potential |
Separate out the angular variables and introduce spinor spherical function |
| Class 13 | free spherical wave |
Formulate the spherical free solution of the Dirac equation |
| Class 14 | energy spectrum of hydrogen atom |
Understand relativistic corrections for hydrogen atom spectrum |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
Lecture notes will be distributed via LMS.
Reference books, course materials, etc.
K. Nishijima, Relativistic Quantum Mechanics, Baifukan (Japanese)
Y. Kawamura, Relativistic Quantum Mechanics, Shokabo (Japanese)
M. Oka, Quantum Mechanics II, Maruzen (Japanese)
'Relativistic Quantum Mechanics and Field Theory', Franz Gross, Wiley-Interscience
Evaluation methods and criteria
Students will be assessed on their understanding of basic ideas in relativistic quantum mechanics and their ability of solving problems.
The scores are based on reports.
Related courses
- PHY.Q208 ： Quantum Mechanics II
- PHY.Q311 ： Quantum Mechanics III
- PHY.E212 ： Electromagnetism II
Prerequisites
No prerequisites are necessary, but enrollment in the related courses is desirable.