HD090000 Quantum Mechanics III

Hiroshima University Syllabus

Japanese

Academic Year 2024Year School/Graduate School School of Science

Lecture Code HD090000 Subject Classification Specialized Education

Subject Name 量子力学III

Subject Name
（Katakana）リョウシリキガク３

Subject Name in
English Quantum Mechanics III

Instructor TANAKA ARATA

Instructor
(Katakana) タナカ　アラタ

Campus Higashi-Hiroshima Semester/Term 3rd-Year,  Second Semester,  Second Semester

Days, Periods, and Classrooms (2nd) Fri3-4：SCI E002 AV

Lesson Style Lecture Lesson Style
(More Details) 　

The traditional way of lecturing with black board.

Credits 2.0 Class Hours/Week 　 Language of Instruction J : Japanese

Course Level 4 : Undergraduate Advanced

Course Area（Area） 25 : Science and Technology

Course Area（Discipline） 06 : Physics

Eligible Students 3rd-Year, Department of Physics

Keywords Angular momentum coupling, the second quantization (an introduction to quantum field theory), charged particles in magnetic field, perturbative treatment of transition process and scattering, the quantum mechanical description of relativistic electrons (the Dirac equation)

Special Subject for Teacher Education 　 Special Subject 　

Class Status
within Educational
Program
(Applicable only to targeted subjects for undergraduate students) This lecture is intended for students who learnt the quantum mechanics in Quantum Mechanics I, II to extend their knowledge and understanding to a higher-level framework of it and to apply it to the real-world phenomena.
Criterion referenced
Evaluation
(Applicable only to targeted subjects for undergraduate students) Physics
（Knowledge and Understanding）
・Knowledge and understanding of specialized field of elementary particle physics, cosmophysics, astrophysics, solid-state physics, condensed matter physics and radiation physics.

Class Objectives
/Class Outline To further deepen the understanding of the quantum mechanics learnt in Quantum Mechanics I, II and to master fundamental knowledge of it required for the fields of elementary particle physics, nuclear physics, astrophysics and condensed matter physics.

Class Schedule Lecture 1 The eigenvalues and eigenfunctions of the angular momentum operator

Lecture 2 Angular momentum coupling

Lecture 3 Applications of angular momentum coupling (examples: systems with the spin-orbit interaction and the exchange interaction).

Lecture 4 Charged particles in magnetic field (1): the Zeeman effect and diamagnetism.

Lecture 5 The eigenvalues and eigenfunctions of the one-dimensional harmonic oscillator and the creation and annihilation operators.

Lecture 6 Quantum many-body systems (1): the second quantization.

Lecture 7 Quantum many-body systems (2): the quantization of the lattice vibration.

Lecture 8 Quantum many-body systems (3): the quantization of the electromagnetic field.

Lecture 9 Quantum many-body systems (4): two electron problem; electronic state of atoms and the periodic table.

Lecture 10 Charged particles in magnetic field (2): local gauge transformation, the Landau quantization and the Aharonov-Bohm effect.

Lecture 11 Perturbative treatment of transition process (1): the Born approximation and the Rutherford scattering

Lecture 12 Perturbative treatment of transition process (2): Fermi's golden rule, emission and absorption of photon, the electric dipole transition and its selection rules.

Lecture 13 General description of the scattering of a particle in a spherical potential: phase shift and the optical theorem.

Lecture 14 The Dirac equation (1): Lorentz invariance and derivation of the Dirac equation, the plane-wave solution (relativistic free electrons).

Lecture 15 The Dirac equation (2): the non-relativistic limit (the magnetic moment of electron and the spin-orbit interaction).

In addition to above lectures, the final examination will be held in the end of this lecture course. Submission of a report is required for every lecture.

Text/Reference
Books,etc. No particular textbook is specified. The titles below are reference books which contain the majority of subjects dealt with in this lecture:
"Modern Quantum Mechanics" by J. J. Sakurai and Jim Napolitano (Cambridge University Press)
"Quantum Mechanics" by Albert Messiah (Dover Books on Physics, English translation)
"Quantum Mechanics: A Shorter Course of Theoretical Physics" by L. D. Landau and‎ E. M. Lifshitz (Pergamon Press, English translation)

PC or AV used in
Class,etc. 　

(More Details) mainly black board; printed materials to supplement the lecture will be provided.

Learning techniques to be incorporated 　

Suggestions on
Preparation and
Review Revision through the subjects learnt in Quantum Mechanics I, II is recommended:
in lesson1, angular momentum, in lesson 5, the harmonic oscillator and in lesson 11, time-dependent perturbation theory.
The basic knowledge of the special theory of relativity is required in lessons 14-15.
Lessons 4, 8, 10 and 12 require the knowledge learnt in Electromagnetism I, II.

Requirements

Grading Method The final examination (70 %) and reports (30 %).

Practical Experience

Summary of Practical Experience and Class Contents based on it

Message Revision through the subjects learnt in Quantum Mechanics I, II is recommended before attending this lecture.

Other

Please fill in the class improvement questionnaire which is carried out on all classes.
Instructors will reflect on your feedback and utilize the information for improving their teaching.

Academic Year	2024Year	School/Graduate School	School of Science
Lecture Code	HD090000	Subject Classification	Specialized Education
Subject Name	量子力学III
Subject Name （Katakana）	リョウシリキガク３
Subject Name in English	Quantum Mechanics III
Instructor	TANAKA ARATA
Instructor (Katakana)	タナカ　アラタ
Campus	Higashi-Hiroshima	Semester/Term	3rd-Year, Second Semester, Second Semester
Days, Periods, and Classrooms	(2nd) Fri3-4：SCI E002 AV
Lesson Style	Lecture	Lesson Style (More Details)
The traditional way of lecturing with black board.
Credits	2.0	Class Hours/Week		Language of Instruction	J : Japanese
Course Level	4 : Undergraduate Advanced
Course Area（Area）	25 : Science and Technology
Course Area（Discipline）	06 : Physics
Eligible Students	3rd-Year, Department of Physics
Keywords	Angular momentum coupling, the second quantization (an introduction to quantum field theory), charged particles in magnetic field, perturbative treatment of transition process and scattering, the quantum mechanical description of relativistic electrons (the Dirac equation)
Special Subject for Teacher Education		Special Subject
Class Status within Educational Program (Applicable only to targeted subjects for undergraduate students)	This lecture is intended for students who learnt the quantum mechanics in Quantum Mechanics I, II to extend their knowledge and understanding to a higher-level framework of it and to apply it to the real-world phenomena.
Criterion referenced Evaluation (Applicable only to targeted subjects for undergraduate students)	Physics （Knowledge and Understanding）・Knowledge and understanding of specialized field of elementary particle physics, cosmophysics, astrophysics, solid-state physics, condensed matter physics and radiation physics.
Class Objectives /Class Outline	To further deepen the understanding of the quantum mechanics learnt in Quantum Mechanics I, II and to master fundamental knowledge of it required for the fields of elementary particle physics, nuclear physics, astrophysics and condensed matter physics.
Class Schedule	Lecture 1 The eigenvalues and eigenfunctions of the angular momentum operator Lecture 2 Angular momentum coupling Lecture 3 Applications of angular momentum coupling (examples: systems with the spin-orbit interaction and the exchange interaction). Lecture 4 Charged particles in magnetic field (1): the Zeeman effect and diamagnetism. Lecture 5 The eigenvalues and eigenfunctions of the one-dimensional harmonic oscillator and the creation and annihilation operators. Lecture 6 Quantum many-body systems (1): the second quantization. Lecture 7 Quantum many-body systems (2): the quantization of the lattice vibration. Lecture 8 Quantum many-body systems (3): the quantization of the electromagnetic field. Lecture 9 Quantum many-body systems (4): two electron problem; electronic state of atoms and the periodic table. Lecture 10 Charged particles in magnetic field (2): local gauge transformation, the Landau quantization and the Aharonov-Bohm effect. Lecture 11 Perturbative treatment of transition process (1): the Born approximation and the Rutherford scattering Lecture 12 Perturbative treatment of transition process (2): Fermi's golden rule, emission and absorption of photon, the electric dipole transition and its selection rules. Lecture 13 General description of the scattering of a particle in a spherical potential: phase shift and the optical theorem. Lecture 14 The Dirac equation (1): Lorentz invariance and derivation of the Dirac equation, the plane-wave solution (relativistic free electrons). Lecture 15 The Dirac equation (2): the non-relativistic limit (the magnetic moment of electron and the spin-orbit interaction). In addition to above lectures, the final examination will be held in the end of this lecture course. Submission of a report is required for every lecture.
Text/Reference Books,etc.	No particular textbook is specified. The titles below are reference books which contain the majority of subjects dealt with in this lecture: "Modern Quantum Mechanics" by J. J. Sakurai and Jim Napolitano (Cambridge University Press) "Quantum Mechanics" by Albert Messiah (Dover Books on Physics, English translation) "Quantum Mechanics: A Shorter Course of Theoretical Physics" by L. D. Landau and‎ E. M. Lifshitz (Pergamon Press, English translation)
PC or AV used in Class,etc.
(More Details)	mainly black board; printed materials to supplement the lecture will be provided.
Learning techniques to be incorporated
Suggestions on Preparation and Review	Revision through the subjects learnt in Quantum Mechanics I, II is recommended: in lesson1, angular momentum, in lesson 5, the harmonic oscillator and in lesson 11, time-dependent perturbation theory. The basic knowledge of the special theory of relativity is required in lessons 14-15. Lessons 4, 8, 10 and 12 require the knowledge learnt in Electromagnetism I, II.
Requirements
Grading Method	The final examination (70 %) and reports (30 %).
Practical Experience
Summary of Practical Experience and Class Contents based on it
Message	Revision through the subjects learnt in Quantum Mechanics I, II is recommended before attending this lecture.
Other
Please fill in the class improvement questionnaire which is carried out on all classes. Instructors will reflect on your feedback and utilize the information for improving their teaching.

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