学部・大学院区分
Undergraduate / Graduate

工学部

時間割コード
Registration Code

0829319

科目区分【日本語】
Course Category

専門科目

科目区分【英語】
Course Category

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

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【日本語】
Department / Program

学科・専攻【英語】
Department / Program

G30 Physics

必修・選択【日本語】
Required / Selected

必修・選択【英語】
Required / Selected

See the "Course List and Graduation Requirements" for your program for your enrolment year.

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

The G30 Physics Program has a small and highly selective student intake, in any year comprising the best few percent of applicants. We are not like regular physics programs in which students may select from a number of different streams (such as students mainly interested in physics research; students mainly interested in teaching physics; students mainly interested in engineering and not fundamental physics; etc.). We only have one stream, and due to the small class size and limited resources, we specifically focus on preparing students for research in theoretical physics, which is what most of our students need in Year 4 and beyond.

Moreover, this is the second part of a full-year, Year 3 course in quantum mechanics: G30 students have already completed two quantum mechanics courses to a level that is comparable to that of some of the best universities.

We do not have time to support NUPACE students who are not strong in physics and mathematics: there is no time for remedial lecturing. Due to the difficulty of some of the topics covered this semester, from our experience with exchange students it is unlikely that exchange students who are not achieving an A grade in both physics and mathematics will be able to keep up, they will struggle and likely lose interest resulting in a waste of their time and ours.

Therefore prospective NUPACE students should note that in principle, only applicants averaging 80% or above in their undergraduate physics and mathematics courses will be permitted to take this course. Students who are unsure may email the lecturer. If necessary, in order to catch up to the required level, prospective NUPACE students will be asked to undertake a self-study course before coming to Nagoya University and during the semester, called "Guided Independent Study -- Further Studies in Quantum Mechanics", which would count as credit towards their NUPACE Exchange Completion Certificate. (Students need at least 15 points to receive this certificate.) Students would be assigned questions to solve from the textbook and would have to submit their solutions to the lecturer to show that they have done the necessary preparation.

DO NOT ARRIVE AT NAGOYA UNIVERSITY EXPECTING THE YEAR 3 G30 PHYSICS COURSES TO CONTRIBUTE TO YOUR DEGREE BECAUSE YOU MIGHT NOT BE PERMITTED TO ATTEND THE COURSE. YOU MUST OBTAIN PRIOR APPROVAL FROM THE COURSE LECTURER. (This holds particularly for QM2, QM3, SP2 and SP3.)

You must be willing to work hard -- this course in the G30 Physics Program is not primarily a cultural experience opportunity in Japan.

到達目標　【日本語】
Objectives of the Course(JPN))

到達目標　【英語】
Objectives of the Course

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 vacuum); introduction to scattering theory.

バックグラウンドとなる科目【日本語】
Prerequisite Subjects

バックグラウンドとなる科目【英語】
Prerequisite Subjects

授業の内容【日本語】
Course Content

授業の内容【英語】
Course Content

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.

成績評価の方法と基準【日本語】
Course Evaluation Method and Criteria

成績評価の方法と基準【英語】
Course Evaluation Method and Criteria

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.

--------------------------------
Necessity / Non-necessity 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.

--------------------------------
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.

--------------------------------
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.

--------------------------------
Notice to Students

Plagiarism (e.g. copying solutions that you have found on the Internet) is an act of academic dishonesty. Cheating in exams (e.g. having lecture notes, assignment solutions or online references open on your computer screen during an online exam) is a serious offence. Copying other people's solutions and claiming them as your own is also an act of academic dishonesty. Nagoya University has a strict policy towards academic dishonesty:

"Acts of academic dishonesty are prohibited during exams, for reports and assignments. If acts of academic dishonesty are discovered, you may be subject to discipline, which may affect your ability to graduate on time."

The punishment for serious breaches (such as cheating in an exam or repeated plagiarism despite a warning) is the loss of all grades from all subjects during the semester and cancellation of any scholarships received.

Even if your course is difficult and it is to be expected that you'll find it hard to finish assignments, it is far better that you submit an honest effort than take the dishonest path. Remember, to be on course for a "B" you only need to score over 70% in the assignments -- and if you paid attention in the tutorials, you would have seen nearly all the problems done for you (in my subjects, at least).

There's no excuse for cheating.

履修条件・注意事項【日本語】
Course Prerequisites / Notes

履修条件・注意事項【英語】
Course Prerequisites / Notes

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.

--------------------------
• It is strongly advised that students concurrently enrol in Physics Tutorial IVb.

• Students must be willing to work hard if they wish to achieve a good, internationally competitive level.

• At the end of this course the lecturer will provide upon request a reading list for students wishing to proceed to the "next level up" in quantum field theory and theoretical condensed matter physics. Students should have a solid understanding of the material covered in both Quantum Mechanics and Statistical Physics.

教科書【日本語】
Textbook

教科書【英語】
Textbook

Shankar, R., 1994, Principles of Quantum Mechanics, 2nd ed., Kluwer Academic/Plenum.

参考書【日本語】
Reference Book

参考書【英語】
Reference Book

Reference Books/Recommended Reading

1. 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.)

2. Cohen-Tannoudji, C., Diu, B., Laloe, F., Quantum Mechanics, Wiley, 1991. Vol. 1 and Vol. 2.

3. Merzbacher, E., Quantum Mechanics, 3rd Ed., Wiley, 1998.
(Merzbacher was one of the best teachers of quantum mechanics.)

4. Landau L. & Lifshitz L., Quantum Mechanics: Non-Relativistic Theory, 3rd Ed., Butterworth-Heinemann (1981).

5. Messiah, A., Quantum Mechanics (2 Volumes), Dover, 2015. (Highly recommended, classic alternative reading. Cheap to buy.)

6. 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.)

授業時間外学習の指示【日本語】
Self-directed Learning Outside Course Hours

授業時間外学習の指示【英語】
Self-directed Learning Outside Course Hours

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 want to achieve a good, internationally competitive level.

--------------------------
Advice

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.

使用言語【英語】
Language used

English

使用言語【日本語】
Language used

授業開講形態等【日本語】
Lecture format, etc.

授業開講形態等【英語】
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【日本語】
Additional measures for remote class (on-demand class)

遠隔授業（オンデマンド型）で行う場合の追加措置【英語】
Additional measures for remote class (on-demand class)

Face to face lectures and tutorials are compulsory. 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.