授業の目的 【日本語】
Goals of the Course(JPN) | | This is a companion course for the Quantum Mechanics III lecture course, which is the second half of a fullyear course. Building on Quantum Mechanics 2, students will learn quantum mechanics at an advanced undergraduate level. The course will build physical intuition of Nature on the quantum scale while improving students’ ability to express physical intuition in mathematical terms and to solve problems.
Students will be adequately prepared with regards to their knowledge of quantum mechanics to undertake further studies in S-lab, E-lab, H-lab, R-lab, TB-lab and other, experimental labs in both the Department of Physics and Department of Applied Physics at Nagoya University. A knowledge of the principles is essential for students interested in experimental physics and theoretical physics. Students from other disciplines, such as chemistry, can also benefit from the deep treatment of quantum phenomena. |
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授業の目的 【英語】
Goals of the Course | | |
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到達目標 【日本語】
Objectives of the Course(JPN)) | | | The course will build physical intuition of Nature on the quantum scale while improving students’ ability to express physical intuition in mathematical terms and to solve problems. |
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到達目標 【英語】
Objectives of the Course | | |
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授業の内容や構成
Course Content / Plan | | Participants are expected to solve problems relating to the lecture course content, and present their solutions on the whiteboard during the tutorial. Students will also submit tutorial assignments, which are set by the Quantum Mechanics III lecturer.This tutorial course covers the same topics as the Quantum Mechanics III
lecture course: Shankar Chapters 11-19 (some parts omitted).
1. Symmetry and Conservation laws in Quantum Mechanics. Translational invariance and its consequences. Active and passive views.
Transformation of operators. Infinitesimal translations. Finite translations. Correspondence with translations in Euclidean space. Time translation invariance; parity invariance; resultant conservation laws.
2. Rotational invariance and its consequences. Rotations in Euclidean space do not commute: derivation of commutation relations between generators of infinitesimal rotations in Euclidean space. Consequence: commutation relations in Hilbert space (and quantum mechanics). Conservation of angular momentum.
3. Rotational invariance and angular momentum. Irreducible representations. Solution of rotationally invariant problems.
The free particle in spherical coordinates.
4. The (spinless) hydrogen atom in coordinate basis; quantization condition. Comparison with experiment; reasons for deviations. Fine structure corrections; hyperfine structure corrections.
5. Spin. Mathematical representation of spin: spinors and their generalization.
Kinematics: properties of the Pauli spin matrices. Spin dynamics.
6. Addition of angular momentum.
Clebsch-Gordon coefficients.
7. Spherical tensor operators and selection rules: Wigner-Eckart Theorem.
Selection rules. Irreducible tensor operators. Explanation of “accidental” degeneracies.
8. The Variational Method and WKB Approximation.
9. Time-independent Perturbation Theory (non-degenerate and degenerate). Dipole selection rule. Example: Stark effect.
10. Time-dependent Perturbation Theory.
Transition rate. Sudden perturbation. Adiabatic perturbation. Periodic perturbation. Fermi’s Golden Rule.
11. Gauge transformations, invariance of QM under gauge transformation.
12. Photoelectric effect in the hydrogen ground state.
13. Elementary introduction to scattering theory. Born approximation. Method of
partial waves. Higher orders in perturbation theory. Schroedinger picture, Interaction picture, Heisenberg picture. |
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履修条件
Course Prerequisites | | | Quantum Mechanics II; or Consent of Instructor |
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関連する科目
Related Courses | | | There is no related courses. |
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成績評価の方法と基準
Course Evaluation Method and Criteria | | | Fortnightly assignments; class participation; fortnightly oral presentation of solutions. (Weighting to be advised.) |
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不可(F)と欠席(W)の基準
Criteria for "Fail (F)" & "Absent (W)" grades | | |
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参考書
Reference Book | | 1. Merzbacher, E., Quantum Mechanics, 3rd Ed., Wiley, 1998.
2. Sakurai, J. J., Napolitano, Jim J., Modern Quantum Mechanics (2nd Ed.), Addison-Wesley, 2010.
3. Cohen-Tannoudji, C., Diu, B., Laloe, F., Quantum Mechanics, Wiley, 1991. 4. Gottfried, K. and Yan, T.-M., 2004, Quantum Mechanics: Fundamentals, Springer. (Advanced reference.) |
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教科書・テキスト
Textbook | | | Shankar, R., 1994, Principles of Quantum Mechanics, 2nd ed., Kluwer Academic/Plenum. |
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課外学習等（授業時間外学習の指示）
Study Load(Self-directed Learning Outside Course Hours) | | |
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注意事項
Notice for Students | | | Students enrolled in Quantum Mechanics III are strongly advised to take this tutorial course. |
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他学科聴講の可否
Propriety of Other department student's attendance | | |
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他学科聴講の条件
Conditions for Other department student's attendance | | |
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レベル
Level | | |
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キーワード
Keyword | | |
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履修の際のアドバイス
Advice | | |
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授業開講形態等
Lecture format, etc. | | |
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遠隔授業（オンデマンド型）で行う場合の追加措置
Additional measures for remote class (on-demand class) | | |
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