学部・大学院区分
Undergraduate / Graduate | | 理学部 | | 時間割コード
Registration Code | | 0680530 | | 科目区分
Course Category | | 専門科目
Specialized Courses | | 科目名 【日本語】
Course Title | | [G30]量子力学３ | | 科目名 【英語】
Course Title | | [G30]Quantum Mechanics III | | コースナンバリングコード
Course Numbering Code | | | | 担当教員 【日本語】
Instructor | | WOJDYLO John Andrew ○ | | 担当教員 【英語】
Instructor | | WOJDYLO John Andrew ○ | | 単位数
Credits | | 2 | | 開講期・開講時間帯
Term / Day / Period | | 春 月曜日 ５時限
Spring Mon 5 | | 授業形態
Course style | | 講義
Lecture | | 学科・専攻
Department / Program | | | | 必修・選択
Compulsory / Selected | | | Compulsory for students intending to join certain research labs; optional for the others. Check with the lab that you have been assigned to. |
| |
授業の目的 【日本語】
Goals of the Course(JPN) | | | | 授業の目的 【英語】
Goals of the Course | | This unit is the second half of a full-year course. Building on Quantum Mechanics II, 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 learn not to be overwhelmed by mathematical symbols, and to discern the simplicity of physical principles expressed by them.
Quantum Mechanics III is an essential step towards higher level study in Condensed Matter Physics (quantum many-body systems), High Energy Physics, Materials Science and many areas of Applied Physics. If taken together with Quantum Mechanics II, Statistical Physics II and Statistical Physics III, students will be well prepared to level up to Condensed Matter Field Theory and Quantum Field Theory in Year 4 or graduate study. Chemistry students have the opportunity to understand foundations of chemistry at a fundamental level and would gain an advantage over their peers.
The main areas covered are:
1. The connection between symmetries and conservation laws
2. The Theory of Angular Momentum
3. Spin and Paramagnetic Resonance
4. The Variational Approach
5. Perturbation Theory: Time Independent Nondegenerate; Time Independent Degenerate; Time Dependent
6. Scattering Theory
NOTICE TO PROSPECTIVE NUPACE (exchange) STUDENTS
Prospective exchange students should be aware that the Nagoya University Department of Physics screens incoming exchange students and rejects or accepts them irrespective of whatever assurances they have been given by their home university or Nagoya University staff in other departments. This means it is possible that you have come all this way to Japan with the intention of continuing your undergraduate degree in Physics but will not be permitted to do so.
If you are interested in coming to study Physics at Nagoya University in the G30 Undergraduate Physics Program then you should contact the lecturer of this course before you make the decision to come to Japan.
WARNING ABOUT THE USE OF GENERATIVE AI
• Assignment exercises are an essential part of both the lecture course and the associated tutorial course. Students are thereby given the opportunity to master a wide variety of technical variations encountered in solving concrete examples of the basic theory, as well as a variety of simple extensions of the basic theory, and simple analytical techniques related to the lecture content but not mentioned in lectures, that extend the scope of problems that students can solve. Mastery of these aspects makes students more attractive to employers or future research labs.
• Reliance on generative AI is harmful to learning. In view of the importance of mastering the assignment exercises, measures will be put in place to ensure that students who rely on generative AI and group discussions to attain high assignment scores without mastering the content will not achieve an inflated final grade: inflated grades are unfair to students who take learning seriously and achieve scholarly independence by genuine hard work. After completing this course, if they do use AI to help with study, students should aim to be capable of critiquing the output from generative AI and evaluating its correctness -- in other words, they must be capable of solving the exercises as well as creative variations of the exercises and lecture content with no help. No employer wants employees who are unable to do this.
Face-to-face lectures, tutorials and exams are opportunities to demonstrate your scholarly independence. Even students who find mathematics difficult can attain at least a "B" grade by engaging in good study habits and learning the lecture content well, and by being honest with themselves and others.
All lecture course exams (Midsemester, End of Semester) are in-class. Students who rely on generative AI and do not master the content will reveal themselves when they are unable to make any meaningful progress with exam questions that are simple repetitions of assignment questions with minor changes or simple creative variations. Even students who have difficulty with mathematics can master such questions if they have good study habits and perseverence. Excessive reliance on generative AI and group discussions wastes time, harms your learning and affects your grades. |
| | 到達目標 【日本語】
Objectives of the Course(JPN)) | | | | 到達目標 【英語】
Objectives of the Course | | The overriding objective of this course is to foster the student's scholarly independence. In order to succeed in this course, students must understand the content sufficiently to have the ability to potentially critique and evaluate the correctness of the output from group work, and generative AI if they use it, relevant to the lecture and assignment content. This is a transferable, real-world skill and, more importantly, mindset: the habit of checking before believing, while possessing the knowledge and technical ability to make the judgement.
Students will have the ability to solve problems such as creative variations of assignment exercises and lecture content with no help, and thereby demonstrate that they are capable of learning STEM knowledge and techniques, and are therefore potentially useful to future employers or university research groups.
Students will be adequately prepared with regards to their knowledge of quantum mechanics to undertake further studies in Sc-lab, St-lab, E-lab, H-lab, QG 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 can also benefit from the deep treatment of quantum phenomena.
Topics include: Symmetry and conservation laws; theory of angular momentum (including addition of angular momentum); solution of rotationally invariant problems; the (spinless) hydrogen atom; Spherical tensor operators and selection rules: Wigner-Eckart Theorem; The Variational Method and WKB Approximation; Time-independent perturbation theory (non-degenerate and degenerate cases); Time-dependent perturbation theory (including scattering off a potential that is a perturbation of the vaccuum); introduction to scattering theory. |
| | 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 in the tutorial course (Physics Tutorial IVb). Students will also submit "tutorial assignments", which are also set by the Quantum Mechanics III lecturer and count towards the tutorial course grade.
The course covers Shankar Chapts 11-19 (some parts omitted); as well as parts of Cohen-Tannoudji et. al, Sakurai, Merzbacher and Gottfried. Some topics are covered in tutorials.
Lecture 1. The Copenhagen Interpretation and Galilean Invariance: Wigner's Theorem; linear and antilinear operators; the time-reversal operator and time-reversal symmetry. Translational invariance and its consequences. Active and passive views. Transformation of operators. Infinitesimal translations; Finite translations. Correspondence with translations in Euclidean space. Translational invariance defined. Consequence: a certain conservation law, and universality of experiments performed at different locations.
Lecture 2. Invariance and conservation laws cont’d. Time translation invariance; parity invariance; resultant conservation laws. Formal correspondence between generators of infinitesimal canonical transformations and generators of infinitesimal unitary transformations.
Lecture 3. 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 for operators defined on Hilbert space (and quantum mechanics). Conservation of angular momentum.
Lecture 4. Rotational invariance and angular momentum. Rotations in 2D: correspondence between those in Euclidean space and Hilbert space. Identifying the generator of infinitesimal rotations in Hilbert space. Active and passive views. Consistency checks: composition of translations and rotations in Hilbert space and Euclidean space. Lie algebra. The eigenvalue problem of L_z. Angular momentum in 3D and the eigenvalue problem of J^2 and J_z. Matrix representation: block diagonal forms and partitioning of Hilbert space.
Lecture 5. Rotational invariance and angular momentum cont’d. Finite rotation operators. Irreducible representations. Orbital angular momentum eigenfunctions in the coordinate basis. Solution of rotationally invariant problems. The free particle in spherical coordinates.
Lecture 6. Solution of rotationally invariant problems cont’d. Radial equation, reduced radial equation, boundary conditions. The (spinless) hydrogen atom in coordinate basis; quantization condition. Eigenfunctions. Also in momentum basis.
Lecture 7. The (spinless) hydrogen atom cont’d. Cause of “unexpected” degeneracy. Comparison with experiment; reasons for deviations. Fine structure corrections; hyperfine structure corrections. Spin. Mathematical representation of spin: spinors and their generalization. Response of vector field Ψ(r) under infinitesimal rotation produces two kinds of generators of infinitesimal rotations, corresponding to orbital and intrinsic angular momentum operators. Kinematics: properties of the Pauli spin matrices. Spin dynamics. Classical magnetic moment suggests form of spin magnetic moment operator. Derivation of Bohr magneton in the Coulomb gauge. Time evolution of spinors.
Lecture 8. Addition of angular momentum. Clebsch-Gordon coefficients. Addition of L and S.
Lecture 9. Spherical tensor operators and selection rules: Wigner-Eckart Theorem. Cartesian tensor operators and irreducible tensor operators. Explanation of “accidental” degeneracies.
Lecture 10. The Variational Method and WKB Approximation. Tunneling amplitudes; bound states.
Lecture 11. Time-independent Perturbation Theory (non-degenerate case). 1st order and 2nd order energy corrections; 1st order correction to wave function. Dipole selection rule. Example: Stark effect.
Lecture 12. Time-independent Perturbation Theory (degenerate case). Time-dependent Perturbation Theory. Transition rate. Sudden perturbation. Adiabatic perturbation. Auger (Radiationless) Transition in helium.
Lecture 13. Time-dependent Perturbation Theory cont’d. Periodic perturbation. Fermi’s Golden Rule. Gauge transformations, invariance of QM under gauge transformation. Photoelectric effect in the hydrogen ground state. Non-examinable: non-Abelian gauge field theories.
Lecture 14. Elementary introduction to scattering theory. Definition of scattering cross-sections. Calculation of the cross-section using probability currents. Expression for the cross-section in terms of scattering amplitude. Born series, Born approximation. Physical interpretation.
Lecture 15. Scattering theory cont’d. Scattering from a central potential using the method of partial waves. Higher orders in perturbation theory: Schroedinger picture, Interaction picture, Heisenberg picture. |
| | 履修条件
Course Prerequisites | | Calculus I; Calculus II; Linear Algebra I; Linear Algebra II; Mathematical Physics I; Mathematical Physics II; Quantum Mechanics II; or Consent of Lecturer.
Students must have passed Quantum Mechanics II to take Quantum Mechanics III. |
| | 関連する科目
Related Courses | | | It is strongly advised that students concurrently enroll in Physics Tutorial IVb. |
| | 「履修取り下げ届」提出の要・不要
Necessity / Unnecessity to submit "Course Withdrawal Request Form" | | | A formal withdrawal form must be signed by the lecturer and submitted to the Student Office by the official withdrawal deadline in May. |
| | 履修取り下げの条件等
Conditions for Course Withdrawal | | A withdrawal request made after the official withdrawal deadline in May will be rejected unless the circumstances are very exceptional.
If Quantum Mechanics III is NOT A COMPULSORY SUBJECT and the student plans never to take Quantum Mechanics III in the future, then a late withdrawal request will be considered. |
| | 成績評価の方法と基準
Course Evaluation Method and Criteria | | Attendance and class performance, attitude: 5%; Weekly quizzes or other written assessment: 30%; Midterm exam: 32.5%; Final Exam: 32.5%
Students will only be permitted to sit the End of Semester Exam if they have submitted at least 4 out of 7 assignments by Lecture 15.
Some exam questions in the lecture course are simple repetitions of either tutorial or lecture assignment questions with minor changes or simple creative variations. If the student is unable to make meaningful progress with such exam questions during the exam, while in the assignment they presented quite a good solution, then the entire assignment corresponding to that question will be deemed to have a mark of 20%.
A certain subset of both Lecture Assignments and Tutorial Assignments must be submitted within a week of the midsemester exam. They will not be accepted after this, and will receive zero marks.
Be aware that mastering the assignments in both the tutorial course and lecture course is essential for performing well in the lecture course exams. You should view assignment work as preparation for the exams.
Students will only be permitted to sit the End of Semester Exam if they have submitted at least 4 out of 7 assignments by the date on which Lecture 15 is held.
Irrespective of how high the total assignment score is, in the two exams the student must demonstrate a sufficient understanding of all the basics: in particular, they must do well in the exam questions that are similar to certain assignment questions or that cover certain simple points in the lecture notes. Therefore, in principle, a student cannot pass the course if they score less than 45% on average in the two exams, even if they score 100% overall in assignments. |
| | 不可(F)と欠席(W)の基準
Criteria for "Fail (F)" & "Absent (W)" grades | | The "Absent (W)" grade is reserved for students who withdraw by the official deadline in May. After that day, a letter grade will be awarded based on marks earned from all assessment during the semester.
If Quantum Mechanics III is NOT A COMPULSORY SUBJECT and the student plans never to take Quantum Mechanics III in the future, then a late withdrawal request will be considered. |
| | 参考書
Reference Book | | Reference Books/Recommended Reading
1. Landau L. & Lifshitz L., Quantum Mechanics: Non-Relativistic Theory, 3rd Ed., Butterworth-Heinemann (1981).
2. Messiah, A., Quantum Mechanics (2 Volumes), Dover, 2015. (Highly recommended, classic alternative reading. Cheap to buy.)
3. Gottfried, K. and Yan, T.-M., 2004, Quantum Mechanics: Fundamentals, Springer.
(Most of this book is too hard for undergraduates but several sections are at the right level and very clear. Consult this book as an authoritative reference.) |
| | 教科書・テキスト
Textbook | | Textbooks
Main textbook:
1. Shankar, R., 1994, Principles of Quantum Mechanics, 2nd ed., Kluwer Academic/Plenum.
Also parts of:
2. Cohen-Tannoudji, C., Diu, B., Laloe, F., Quantum Mechanics, Wiley, 1991. Vol. 1 and Vol. 2.
3. Sakurai, J. J., Napolitano, Jim J., Modern Quantum Mechanics (2nd Ed.), Addison-Wesley, 2010. (This book complements, and at times supersedes, the treatment in Shankar.)
4. Merzbacher, E., Quantum Mechanics, 3rd Ed., Wiley, 1998. |
| | 課外学習等（授業時間外学習の指示）
Study Load(Self-directed Learning Outside Course Hours) | | Study Load (Self-directed Learning Outside Course Hours)
• This is a challenging course that requires a substantial time commitment.
• This course is part of your training to be a professional researcher. You are expected to revise the lecture notes, read and work through the textbook, and solve assignment problems outside lecture hours. You cannot learn physics by only attending lectures. The exams will consist of questions covering both lecture notes and assignments.
• Students must be willing to work hard if they wish to achieve a good, internationally competitive level. |
| | 注意事項
Notice for Students | | • Some exam questions in the lecture course are simple repetitions of either tutorial or lecture assignment questions with minor changes or simple creative variations. If the student is unable to make meaningful progress with such exam questions during the exam, while in the assignment they presented quite a good solution, then the entire assignment corresponding to that question will be deemed to have a mark of 20%.
• A certain subset of both Lecture Assignments and Tutorial Assignments must be submitted within a week of the midsemester exam. They will not be accepted after this, and will receive zero marks.
• Students will only be permitted to sit the End of Semester Exam if they have submitted at least 4 out of 7 assignments by the date on which Lecture 15 is held.
• Irrespective of how high the total assignment score is, in the two exams the student must demonstrate a sufficient understanding of all the basics: in particular, they must do well in the exam questions that are similar to certain assignment questions or that cover certain simple points in the lecture notes. Therefore, in principle, a student cannot pass the course if they score less than 45% on average in the two exams, even if they score 100% overall in assignments.
WARNING ABOUT THE USE OF AI
• Despite any rules and better ethical judgment, many of you will rely on AI (ChatGPT, Gemini, Sonnet, Claude etc.) to solve your assignment problems. Be aware that besides constituting academic misconduct and dishonesty, such use of AI is detrimental to your learning: among other things, you will lack the experience of getting stuck and digging your way out of a problem using your own knowledge, tenacity, ingenuity and creativity. You will not learn resilience in the field of study. The examinations are designed to test the quality of your learning, your ability to bring together multiple threads dealt with in lectures and assignments, your ability to interpret the equations and unify your understanding, to seek connections and dig your way out of a seeming dead end when solving a problem. You will not learn this by relying on AI. You will do very well in assignments but very poorly in the exams.
• Reliance on generative AI is harmful to learning. In view of the importance of mastering the assignment exercises, measures will be put in place to ensure that students who rely on generative AI and group discussions to attain high assignment scores without mastering the content will not achieve an inflated final grade: inflated grades are unfair to students who take learning seriously and achieve scholarly independence by genuine hard work. After completing this course, if they do use AI to help with study, students should aim to be capable of critiquing the output from generative AI and evaluating its correctness -- in other words, they must be capable of solving the exercises as well as creative variations of the exercises and lecture content with no help. No employer wants employees who are unable to do this.
Face-to-face lectures, tutorials and exams are opportunities to demonstrate your scholarly independence. Even students who find mathematics difficult can attain at least a "B" grade by engaging in good study habits and learning the lecture content well, and by being honest with themselves and others.
All lecture course exams (Midsemester, End of Semester) are in-class. Students who rely on generative AI and do not master the content will reveal themselves when they are unable to make any meaningful progress with exam questions that are simple repetitions of assignment questions with minor changes or simple creative variations. Even students who have difficulty with mathematics can master such questions if they have good study habits and perseverence. Excessive reliance on generative AI and group discussions wastes time, harms your learning and affects your grades. |
| | 他学科聴講の可否
Propriety of Other department student's attendance | | | Students from any department are welcome as long as they have the necessary grounding in mathematics and physics. |
| | 他学科聴講の条件
Conditions for Other department student's attendance | | | Students from any department are welcome as long as they have the necessary grounding in mathematics and physics. |
| | レベル
Level | | | | キーワード
Keyword | | | | 履修の際のアドバイス
Advice | | Advice
• Focus on your undergraduate studies. Resist distractions. Learn as much as you can. This period in your life is a golden opportunity that might never be repeated.
• It is strongly advised that students concurrently enroll in Physics Tutorial IVb.
• No solutions are handed out in class. It pays to come prepared and pay attention during the tutorial.
• Students must be willing to work hard if they wish to achieve a good, internationally competitive level.
• Assignment exercises are an essential part of both the lecture course and the associated tutorial course. Students are thereby given the opportunity to master a wide variety of technical variations encountered in solving concrete examples of the basic theory, as well as a variety of simple extensions of the basic theory, and simple analytical techniques related to the lecture content but not mentioned in lectures, that extend the scope of problems that students can solve. Mastery of these aspects makes students more attractive to employers or future research labs.
• Reliance on generative AI is harmful to learning. In view of the importance of mastering the assignment exercises, measures will be put in place to ensure that students who rely on generative AI and group discussions to attain high assignment scores without mastering the content will not achieve an inflated final grade: inflated grades are unfair to students who take learning seriously and achieve scholarly independence by genuine hard work. After completing this course, if they do use AI to help with study, students should aim to be capable of critiquing the output from generative AI and evaluating its correctness -- in other words, they must be capable of solving the exercises as well as creative variations of the exercises and lecture content with no help. No employer wants employees who are unable to do this.
Face-to-face lectures, tutorials and exams are opportunities to demonstrate your scholarly independence. Even students who find mathematics difficult can attain at least a "B" grade by engaging in good study habits and learning the lecture content well, and by being honest with themselves and others.
All lecture course exams (Midsemester, End of Semester) are in-class. Students who rely on generative AI and do not master the content will reveal themselves when they are unable to make any meaningful progress with exam questions that are simple repetitions of assignment questions with minor changes or simple creative variations. Even students who have difficulty with mathematics can master such questions if they have good study habits and perseverence. Excessive reliance on generative AI and group discussions wastes time, harms your learning and affects your grades. |
| | 授業開講形態等
Lecture format, etc. | | Face to face lectures and tutorials are compulsory (other than in exceptional circumstances; e.g. COVID infection). However, in order to record a video of the lecture -- including student interaction with each other and with the lecturer -- the lectures will simultaneously be carried out online using MS Teams. Students are therefore requested to bring their laptop or tablet to the lecture room. Make sure it has a microphone. Bring an electrical cord. For many G30 students, English is a 2nd or even 3rd language, so video recordings are an invaluable learning aid.
Live lectures via MS Teams (face-to-face and online). Before the start of semester students should ensure that they have correctly installed MS Teams using their THERS (国立大学法人東海国立大学機構 ) email account.
NUPACE students should contact Professor John Wojdylo before the start of semester for assistance with installing Teams correctly. |
| | 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) | | All lectures will be live face-to-face and online via MS Teams. Face-to-face attendance is compulsory (barring exceptional circumstances such as COVID infection).
A lecture video will be available immediately after each lecture to help with student revision.
The lecturer will be available to answer questions via Teams chat. |
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