2025 (Current Year) Faculty Courses School of Engineering Undergraduate major in Electrical and Electronic Engineering
Quantum Mechanics
- Academic unit or major
- Undergraduate major in Electrical and Electronic Engineering
- Instructor(s)
- Tetsuo Kodera / Takayuki Iwasaki
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 1-2 Tue / 1-2 Fri
- Class
- -
- Course Code
- EEE.D201
- Number of credits
- 200
- Course offered
- 2025
- Offered quarter
- 1Q
- Syllabus updated
- Mar 19, 2025
- Language
- Japanese
Syllabus
Course overview and goals
This course addresses quantum mechanics, the foundation of modern engineering. The instructor will explain that particles such as electrons behave as waves in microscopic systems and lead to the Schrödinger equation, which mathematically describes the wave-like behavior of matter. The instructor will also discuss subjects such as the properties of wave functions, operations for quantization, and the uncertainty principle. The Schrödinger equation will be solved to investigate bound states in quantum wells and quantum tunneling in potential barriers. Further the instructor will discuss harmonic oscillators and central force fields, leading to concepts and mathematics specific to quantum mechanics, such as state vectors and angular momentum. The instructor will reveal the structure of hydrogen atoms and explain the electron configuration of many-electron systems. Also, perturbation theory will be discussed as a method for approximating the Schrödinger equation.
Quantum mechanics is necessary in the field of chemistry and materials engineering related to such things as semiconductors to analyze the behavior of electrons and holes. Quantum computers and other quantum information processing also require knowledge of quantum mechanics. On the other hand, quantum mechanics is said to be difficult to grasp for introductory students. This course provides explanations for an efficient mastery of quantum mechanics, and students will develop a foundation for utilizing and applying it in various fields by completing numerous exercise problems.
Course description and aims
By taking this course, you are able to
(1) acquire the innovative view of nature being created by quantum mechanics,
(2) understand the concepts specific to quantum mechanics of the wave probability, state vectors, the uncertainty principle, the tunnel effect, and spin,
(3) solve the Schrödinger equation for square well potential, the harmonic oscillator, and the central force field,
(4) apply the knowledge of linear algebra including matrices and eigenvalues, and special functions,
(5) understand the algebra of angular momenta and visualize the structure of hydrogen atom, and
(6) acquire an approximate means for problems that cannot be exactly solved.
Keywords
Schrödinger equation, quantum well, tunnel effect, harmonic oscillator, central force field, perturbation theory
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
- ・Applied specialist skills on EEE
Class flow
Read the sections of the textbook corresponding to each class in advance. In each class, basic points are explained and exercises are done. Do the end-of-section problems after class.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | The Planck's Quantum Hypothesis, Einstein's Light Quanta, the Photoelectric Effect | Read the collapse of classical mechanics and the rise of quantum mechanics, |
| Class 2 | The Wave-Particle Duality | Learn de Broglie waves. |
| Class 3 | Wave Packets and Wave Functions, The Schrödinger Equation | Learn the wave probability, and derive the Schrödinger equation. |
| Class 4 | Observables and Operators, The Heisenberg Uncertainty Principle | Learn the relationship between observables and Hermitian operators and how to calculate expectation values, and derive the uncertainty relation. |
| Class 5 | Eigenvalues and Eigenfunctions, Free Particles | Derive the energy and momentum eigenstates from the time-independent Schrödinger equation. |
| Class 6 | Potential Well | Solve the one-dimensional square well potential problems, and learn the characteristics of eigenfunctions including the complete system and the basis, and Parity. |
| Class 7 | Learning achievement questions | Test the level of understanding and self-evaluate achievement for classes 1–6. |
| Class 8 | The Tunnel Effect | Learn tunneling through a thin potential barrier and the resonant transmission. |
| Class 9 | The Harmonic Oscillator | Solve the energy eigenvalues of the harmonic oscillator and express the eigenfunctions with the Hermite polynomial, and derive the zero-point oscillation. |
| Class 10 | Creation and Annihilation Operators, State Vectors | Solve the harmonic oscillator problem with the operator method, and acquire the ket notation of state vectors and the matrix notation of operators. |
| Class 11 | The Central Force Field | Express the Schrödinger equation with spherical coordinates, and learn angular momentum operators and spherical harmonics. |
| Class 12 | The Hydrogen Atom | Learn the directional quantization, and express the eigenfunctions of the hydrogen atom with the Laguerre polynomial. |
| Class 13 | Spin and the Pauli Exclusion Principle | Derive spin angular momenta with commutation relations and ladder operators, and learn the Pauli exclusion principle. |
| Class 14 | Perturbation Theory | Solve the Schrödinger equation under a perturbation. |
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)
Haruhiko Ito, Quantum Mechanics for Students of Science and Engineering, e-book edition, Kodansha Scientific (Japanese).
Reference books, course materials, etc.
Isao Harada, Tadao Sugiyama, Quantum Mechanics I (Kodansha Basic Physics Series), Kodansha ISBM 4061572067
Feynman, Leighton, Sands, The Feynman Lectures on Physics, Vol. III: Quantum Mechanics, Basic Books ISBN 9780465025015
Evaluation methods and criteria
You are assessed by the comprehension of the concepts unique to quantum mechanics and the solution of the Schrödinger equation.
The point allocation is 20 % for assignments, 40 % for the learning achievement questions, and 40 % for the final exam.
Related courses
- LAS.C105 ： Basic Quantum Chemistry
- EEE.D211 ： Semiconductor Physics
- EEE.D351 ： Electron Devices I
- EEE.D352 ： Electron Devices II
- EEE.D301 ： Electrical and Electronics Materials
Prerequisites
Calculus, Linear Algebra, and Mechanics are needed for this course.