| Course title | |||||
| 量子化学Ⅰ [Quantum ChemistryⅠ] | |||||
| Course category | technology speciality courses,ets. | Requirement | Credit | 2 | |
| Department | Year | 2～4 | Semester | 1st | |
| Course type | 1st | Course code | 022306 | ||
| Instructor(s) | |||||
| 久世 信彦 [KUZE Nobuhiko] | |||||
| Facility affiliation | Graduate School of Engineering | Office | Email address | ||
| Course description |
|
[Purpose] Quantum chemistry is a field of physical chemistry that examines various properties of molecules theoretically and experimentally based on quantum mechanics which is completely different from classical mechanics. Spectroscopy, which is based on the quantum mechanics, is widely used in the many scientific fields such as the material productions. In this lecture, you will learn the basic principle of quantum mechanics as well as the fundamental about the quantum theory of translation, vibration, and rotation of molecules. Then you can understand the nature of quantum chemistry and spectroscopic principles of atoms and molecules. Therefore, this lecture is belong to the basis courses of the curriculum policy, which is a first step to learn the contents of the advanced courses such as "Quantum chemistry II" and "Structural chemistry" [Contents] We begin with a few historical experiments which were important to a birth of the quantum mechanics. Next you will learn the basic topic of the quantum mechanics such as wavefunction, Hamilton operator, and Schroedinger equation as well as the mathematical tools to understand these topics. Then you will learn the basic theories on translational, vibrational and rotational motions to understand the principal concepts of spectroscopy and quantum chemistry on atoms and molecules. |
| Expected Learning |
|
This course aims the next four items for the expected learning by referring the diploma policy A, getting the basic skills about the natural science. (1) You can understand the difference of physical description in classical mechanics and quantum mechanics. (2) You can understandi of the wavefunction, Hamilton operator, and Schroedinger equation. (3) You and derive and calculate the Schroedinger equation in simple cases, then find the corresponding wavefunction and energy level. (4) You can understand of the quantization of the translational, vibrational and rotational energies. Then you can solve the mathematical exercises for these topics. |
| Course schedule |
|
1. Introduction The failure of classical physics (Text (Atkins Physical Chemistry 8th Edition): Section 8.1) Origin of quantum mechanics, blackbody radiation, photoelectric effect, spectrum of hydrogen atoms 2. Duality of light and particles (Text: Section 8.2) Compton scattering and particle properties of light, wave nature of matter and de Broglie wave, early quantum theory 3. Schroedinger equation (Text: Sections 8.3-8.4) Hamilton operator, wavefunction, Schrodinger equation in a steady state 4. Information included in the wavefunction (1) (Text: Section 8.5) Operators, eigenvalues and eigenfunctions, Hermitian operators 5. Information included in the wavefunction (2) (Text: Section 8.5) Expression of motion, observable and expectation value in quantum mechanics 6. Uncertainty principle and the basic principles of quantum mechanics (Text: Sections 8.6-8.7) Uncertainty principle, commutative operator 7. Translation (1) (Text: Section 9.1) Particle in one-dimensional box, boundary condition and normalization, shape and nature of the wavefunction, energy level 8. Translation (2) (Text: Sections 9.2-9.3) Particle in three-dimensional box, variable separation, degeneracy, tunneling motion 9. Vibrational (Text: Sections 9.4-9.5) The wavefunction and energy levels for harmonic oscillator, Hermitian polynomial. 10. Rotation (1) (Text: Section 9.6) Rotational motion on a plane, polar coordinates and coordinate transformation 11 Rotation (2) (Text: Section 9.7) Rotation in the three-dimensional space, Legendre function and spherical harmonic function 12. Angular momentum and spin (1) (Text: Sections 9.7-9.8) Angular momentum, space quantization, vector model 13. Angular momentum and spin (2) (Text: Section 9.8) Stern-Gerlach experiment, spin function 14. Approximation method: perturbation theory (Text: Sections 9.9-9.10) Time-independent perturbation theory, time-dependent perturbation theory 15. Summary Final exam and comments As a preparation / review each time, I will present a keyword explanation and a task to solve the exercise problem. |
| Prerequisites |
| Related courses: mathematics, classical mechanics, physics of vibration and wave, electromagnetism, inorganic chemistry Ⅰ |
| Required Text(s) and Materials |
| Atkins Physical Chemistry 8th and 10th Editions, Tokyo Kagaku Doujin |
| References |
| Physical Chemistry Quanta, Matter, and Change, P. Atkins, J. de Paula, R. Friedman, Oxford, 2014 |
| Assessment/Grading |
| Reports（10×2 = 20%） and Final exam (80%) |
| Message from instructor(s) |
| In this lecture, many calculations such as derivations of numerous expressions, differentiation and integration will be appeared. While I would like to solve these calculations as much as possible during the lecture, I will assign the exercises as a subject of preliminary review for a full understanding of lecture contents. Therefore, I hope to positively address these issues. |
| Course keywords |
| Quantum mechanics, Hamiltonian operator, Schroedinger equation, eigenvalue, eigenfunction, wavefunction, uncertainty principle |
| Office hours |
| Please contact me during the class, after the class or e-mail (n-kuze@sophia.ac.jp). |
| Remarks 1 |
| Remarks 2 |
| Related URL |
| Lecture Language |
| Japanese |
| Language Subject |
| Last update |
| 3/22/2019 5:05:55 PM |