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- Common courses
- Liberal arts and basic science courses
- Academic unit or major
- Undergraduate major in Physics
- Instructor(s)
- Sekizawa Kazuyuki
- Class Format
- Lecture / Exercise
- Media-enhanced courses
- Day/Period(Room No.)
- -
- Group
- -
- Course number
- PHY.L210
- Credits
- 2
- Academic year
- 2024
- Offered quarter
- 4Q
- Syllabus updated
- 2024/3/14
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
-
Course description and aims
"Experiment", "Theory", and "Numerical Calculation" are regarded as three pillars of modern physics and the latter plays an important role in exploring fundamental laws of the nature. In this lecture, students aim to acquire basic skills of programming, numerical calculation, as well as data analysis, which are applicable to cutting-edge studies, through extensive hands-on exercises related to various phenomena.
Student learning outcomes
Students are expected:
- to learn various techniques to computationally solve equations and to acquire basic knowledge of numerical calculations,
- to learn basics of programming and data analysis and to gain ability to write a computational code from scratch,
- to be able to numerically solve any equations, expressing them on a computational code, and applying appropriate techniques.
Keywords
Fortran, Programming, Numerical Calculation, Simulation, Computational Fluid Dynamics (CFD), Quantum Mechanics, Superfluidity
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | ✔ Critical thinking skills | ✔ Practical and/or problem-solving skills |
Class flow
Roughly 1/3 of each class will be a lecture on basic concepts, required knowledge, and important points. The rest of each class will be adopted to hands-on exercises on practical programming and computation.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Preparing Computation Environment I | Prepare computation environment on a shared PC or your PC. |
| Class 2 | Preparing Computation Environment II | Prepare computation environment on a shared PC or your PC. Learn basics of how to use a terminal. |
| Class 3 | An Introduction to Fortran Programming I: Basic Grammars | Learn basic knowledge on how to write a computational code with Fortran language. |
| Class 4 | An Introduction to Fortran Programming II: Basic Exercises and Monte Carlo Calculation of the Circle Ratio | Solve several basic problems with Fortran. Write a computational code to calculate the circle ratio utilizing random numbers. |
| Class 5 | Finite-Difference Method and Its Accuracy: Diffusion and Advection Equations | Understand how to solve a differential equation with the finite difference method. Analyze accuracy and stability of finite-difference schemes by numerically solving a 1D diffusion and advection equations. |
| Class 6 | An Introduction to Computational Fluid Dynamics (CFD): Vorticity Equation and Kármán Vortex Street | Learn basic concepts of Computational Fluid Dynamics (CFD). Understand the vorticity equation. Generate Kármán vortex street by numerically solving the 2D vorticity equation. |
| Class 7 | Computational Techniques for Equations of Motion: Single and Double Pendulums | Understand several methods to numerically solve classical equations of motion. Perform numerical simulations for a single pendulum. |
| Class 8 | Computational Techniques for Equations of Motion: N-fold Pendulum | Install a comprehensive library, LAPACK, for manipulating linear-algebra-related calculations. Perform numerical simulations for an N-fold pendulum with the aid of LAPACK. |
| Class 9 | Computational Techniques for a Time-Independent Schrödinger Equation I: Numerov's Method | Understand the Schrödinger equation for electronic wave functions in a hydrogen atom and Numerov's method. Calculate (trial) electronic wave functions in a hydrogen atom by numerically solving a radial Schrödinger equation using Numerov's method. |
| Class 10 | Computational Techniques for a Time-Independent Schrödinger Equation II: Shooting and Bisection Methods | Calculate eigenfunctions and eigenenergies of electrons in a hydrogen atom by numerically solving the radial Schrödinger equation using Numerov's method, imposing boundary conditions near the origin and at large distance using shooting and bisection methods. |
| Class 11 | Computational Techniques for a Time-Independent Schrödinger Equation III: Matrix Diagonalization | Understand the matrix representation of the 1D Schrödinger equation. Understand the Jacobi method to diagonalize a real symmetric matrix. Calculate eigenvalues and eigenvectors for 1D Schrödinger equation by diagonalizing its Hamiltonian matrix. |
| Class 12 | Computational Techniques for a Time-Dependent Schrödinger Equation: Explicit and Implicit Methods, and Potential Scattering of a Wave Packet | Understand explicit and implicit methods for solving the time-dependent Schrödinger equation (TDSE). Analyze time evolution of a wave packet scattered by a potential by numerically solving a 1D TDSE using the Taylor expansion method. |
| Class 13 | Introduction to Quantum Hydrodynamics I: 1D TDGPE and Generation of a Dark Solition | Understand time-dependent Gross-Pitaevskii equation (TDGPE) for superfluid dynamics. Generate a dark soliton by numerically solving 1D TDGPE. |
| Class 14 | Introduction to Quantum Hydrodynamics II: 2D TDGPE and Generation of Quantum Vortices | Understand basic properties of topological excitation modes of superfluid. To know physical phonomena related to topological excitations of superfluid, such as solitons or quantum vortices. Generate quantum vortices by numerically solving 2D TDGPE. |
Out-of-Class Study Time (Preparation and Review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for each class and another 100 minutes reviewing class content after each class (including assignments). They should do so by referring to textbooks and other course materials.
Textbook(s)
Lecture slides and sample codes distributed by the instructor.
Reference books, course materials, etc.
Not specified.
Assessment criteria and methods
By monthly report.
Related courses
- PHY.Q207 ： Introduction to Quantum Mechanics
- LAS.M106 ： Linear Algebra II
- PHY.C442 ： Superfluidity
Prerequisites (i.e., required knowledge, skills, courses, etc.)
No prerequisites.
Contact information (e-mail and phone) Notice : Please replace from "[at]" to "@"(half-width character).
Kazuyuki Sekizawa
sekizawa at phys.titech.ac.jp
2463
Office hours
Students can ask any questions at any times via Slack or email.
