HC085000 Quantum Mechanics I

Hiroshima University Syllabus

Japanese

Academic Year 2024Year School/Graduate School School of Science

Lecture Code HC085000 Subject Classification Specialized Education

Subject Name 量子力学I

Subject Name
（Katakana）リョウシリキガク１

Subject Name in
English Quantum Mechanics I

Instructor ISHIKAWA KENICHI

Instructor
(Katakana) イシカワ　ケンイチ

Campus Higashi-Hiroshima Semester/Term 2nd-Year,  Second Semester,  Second Semester

Days, Periods, and Classrooms (2nd) Thur7-10：SCI E102

Lesson Style Lecture Lesson Style
(More Details) 　

Lecturer explains the contents via text manuscript on slides.
This class consists of two parts/slots,  lecture part (1st slot) and exercise part (2nd slot).　Attendees should learn and work on questions in the second part interactively in the class room.  This class uses MS teams and Moodle.

Credits 3.0 Class Hours/Week 　 Language of Instruction J : Japanese

Course Level 2 : Undergraduate Low-Intermediate

Course Area（Area） 25 : Science and Technology

Course Area（Discipline） 06 : Physics

Eligible Students Semester No. 4

Keywords Quantum Mechanics (introductory part)

Special Subject for Teacher Education 　 Special Subject 　

Class Status
within Educational
Program
(Applicable only to targeted subjects for undergraduate students) Learn the introductory part of  Quantum Mechanics, and prepare for the "Quantum Mechanics II".
Criterion referenced
Evaluation
(Applicable only to targeted subjects for undergraduate students) Physics
（Knowledge and Understanding）
・Knowledge and understanding of physical mathematics, mechanics, electromagnetism, thermodynamics, statistical mechanics and quantum mechanics.

Class Objectives
/Class Outline To understand Quantum Mechanics, we learn the introductory part of it aiming for theoretical understanding on the quantum phenomena in this class.
Understanding of  Schroedinger equation,  properties and meaning of wave function, and the quantum mechanical properties of an electron in a Hydrogen atom.

Class Schedule 1.  Wave--particle duality, particle-ness and wave-ness : Learn the historical part of the early development of Quantum mechanics.
2. Fourier series : Using the Fourier series analysis, we learn the duality of the wave-ness and particle-ness.
3. Fourier transformation : Using the Fourier transformation analysis, we learn the duality of the wave-ness and particle-ness.
4. Phase velocity and Group velocity : Learn the properties for the plane wave and packet wave, in particular, the phase velocity and the group velocity. We relate the group velocity to the particle velocity in terms of the wave--particle duality.
5. Developing Schroedinger equation, interpretation of the wavefunction, conservation of the probability and flow : We introduce the Schroedinger equation based on the wave--particle duality relation learned in the classes No1--No4. We learn the probability interpretation for the wave function in quantum mechanics. The flow and conservation of probability is established.
6. Ehrenfest's theorem : We learn the correspondence between quantum mechanics and classical mechanics on the expectation value of observables.
7. Obserbables and commutation relation : We learn the physical observables in quantum mechanics. We learn the quantum mechanical interpretation of the eigenvector and eigenvalue of operators.
8. Free particle wave function in one-dimensional space : We extract the properties of the Schroedinger equation from this explicit example.
9. Scattering problem in one-dimensional space, tunneling effect : We learn the quantum phenomena occurring in this situation.
10. Bound state in a box : Learn the method to solve the Schroedinger equation for bound states.
11. Harmonic oscillator : Learn the general properties of the one-dimensional Schroedinger equation for bound states. We then solve the one-dimensional quantum Harmonic oscillator.
12. Spherical coordinate system : We remind the spherical coordinate system for the three-dimensional Schroedinger equation having a spherically symmetric potential.
13. Schroedinger equation for spherically symmetric system : We prepare for solving Schroedinger equations with the spherical symmetry by employing the method of separation of variables for the PDE. We also learn the spherical harmonic functions and the relation to the angular momentum.
14. Spectrum of a Hydrogen atom: We solve the quantum properties of a Hydrogen atom by solving the Schroedinger equation with the Coulomb potential. We also learn the phenomenological properties of the spectrum of hydrogen in terms of the quantum mechanics that we have learned so far.

15. Final Exam.

One class consists of two slots, the first slot is assigned to the lecture part and the second to the exercise part.
The class materials (lecture note and problems for exercise) will be distributed via Moolde. The answers for the exercise should be submitted through Moodle.
Final examination for grading is assigned in the last class.
15. Final Exam.

The attendance at the exercise and the submission of answers are mandatory as the class credit unit is given to the pair of lecture and exercise parts.

Text/Reference
Books,etc. I use
猪木慶治、川合光　共著「量子力学I」（講談社サイエンティフィック）
(in Japanese).
Another textbook,
Leonard I. Schiff, "Quantum Mechanics", McGraw-Hill; 3Rev Ed edition (1968)
is sufficient.

PC or AV used in
Class,etc. 　

(More Details) Knowledge retention will be checked in the exercise  part via problem assignment.
Hand-written answer manuscript to the assignment should be submitted to Moodle in a PDF/JPEG/PNG file form scanned by a camera or a scanner.  You must pass the problem assignment during the exercise time.

Learning techniques to be incorporated 　

Suggestions on
Preparation and
Review I will assign exercise problems in the class.  You are required to solve and exercise the problems in the class.
You are also required to review concepts lectured in this class by referencing text books and discussion with class members to understand the concepts.

Requirements

Grading Method Final Examination is mandatory. The weight ratio for the credit is
Exercise problem (about 30%), Final exam (about 60%).
The attendance at the exercise and the submission of answers are mandatory as the class credit unit is given to the pair of lecture and exercise parts.
When the final exam was on-lined, the grading will be examined by an extra/final homework report.

Practical Experience

Summary of Practical Experience and Class Contents based on it

Message

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	HC085000	Subject Classification	Specialized Education
Subject Name	量子力学I
Subject Name （Katakana）	リョウシリキガク１
Subject Name in English	Quantum Mechanics I
Instructor	ISHIKAWA KENICHI
Instructor (Katakana)	イシカワ　ケンイチ
Campus	Higashi-Hiroshima	Semester/Term	2nd-Year, Second Semester, Second Semester
Days, Periods, and Classrooms	(2nd) Thur7-10：SCI E102
Lesson Style	Lecture	Lesson Style (More Details)
Lecturer explains the contents via text manuscript on slides. This class consists of two parts/slots, lecture part (1st slot) and exercise part (2nd slot).　Attendees should learn and work on questions in the second part interactively in the class room. This class uses MS teams and Moodle.
Credits	3.0	Class Hours/Week		Language of Instruction	J : Japanese
Course Level	2 : Undergraduate Low-Intermediate
Course Area（Area）	25 : Science and Technology
Course Area（Discipline）	06 : Physics
Eligible Students	Semester No. 4
Keywords	Quantum Mechanics (introductory part)
Special Subject for Teacher Education		Special Subject
Class Status within Educational Program (Applicable only to targeted subjects for undergraduate students)	Learn the introductory part of Quantum Mechanics, and prepare for the "Quantum Mechanics II".
Criterion referenced Evaluation (Applicable only to targeted subjects for undergraduate students)	Physics （Knowledge and Understanding）・Knowledge and understanding of physical mathematics, mechanics, electromagnetism, thermodynamics, statistical mechanics and quantum mechanics.
Class Objectives /Class Outline	To understand Quantum Mechanics, we learn the introductory part of it aiming for theoretical understanding on the quantum phenomena in this class. Understanding of Schroedinger equation, properties and meaning of wave function, and the quantum mechanical properties of an electron in a Hydrogen atom.
Class Schedule	1. Wave--particle duality, particle-ness and wave-ness : Learn the historical part of the early development of Quantum mechanics. 2. Fourier series : Using the Fourier series analysis, we learn the duality of the wave-ness and particle-ness. 3. Fourier transformation : Using the Fourier transformation analysis, we learn the duality of the wave-ness and particle-ness. 4. Phase velocity and Group velocity : Learn the properties for the plane wave and packet wave, in particular, the phase velocity and the group velocity. We relate the group velocity to the particle velocity in terms of the wave--particle duality. 5. Developing Schroedinger equation, interpretation of the wavefunction, conservation of the probability and flow : We introduce the Schroedinger equation based on the wave--particle duality relation learned in the classes No1--No4. We learn the probability interpretation for the wave function in quantum mechanics. The flow and conservation of probability is established. 6. Ehrenfest's theorem : We learn the correspondence between quantum mechanics and classical mechanics on the expectation value of observables. 7. Obserbables and commutation relation : We learn the physical observables in quantum mechanics. We learn the quantum mechanical interpretation of the eigenvector and eigenvalue of operators. 8. Free particle wave function in one-dimensional space : We extract the properties of the Schroedinger equation from this explicit example. 9. Scattering problem in one-dimensional space, tunneling effect : We learn the quantum phenomena occurring in this situation. 10. Bound state in a box : Learn the method to solve the Schroedinger equation for bound states. 11. Harmonic oscillator : Learn the general properties of the one-dimensional Schroedinger equation for bound states. We then solve the one-dimensional quantum Harmonic oscillator. 12. Spherical coordinate system : We remind the spherical coordinate system for the three-dimensional Schroedinger equation having a spherically symmetric potential. 13. Schroedinger equation for spherically symmetric system : We prepare for solving Schroedinger equations with the spherical symmetry by employing the method of separation of variables for the PDE. We also learn the spherical harmonic functions and the relation to the angular momentum. 14. Spectrum of a Hydrogen atom: We solve the quantum properties of a Hydrogen atom by solving the Schroedinger equation with the Coulomb potential. We also learn the phenomenological properties of the spectrum of hydrogen in terms of the quantum mechanics that we have learned so far. 15. Final Exam. One class consists of two slots, the first slot is assigned to the lecture part and the second to the exercise part. The class materials (lecture note and problems for exercise) will be distributed via Moolde. The answers for the exercise should be submitted through Moodle. Final examination for grading is assigned in the last class. 15. Final Exam. The attendance at the exercise and the submission of answers are mandatory as the class credit unit is given to the pair of lecture and exercise parts.
Text/Reference Books,etc.	I use 猪木慶治、川合光　共著「量子力学I」（講談社サイエンティフィック） (in Japanese). Another textbook, Leonard I. Schiff, "Quantum Mechanics", McGraw-Hill; 3Rev Ed edition (1968) is sufficient.
PC or AV used in Class,etc.
(More Details)	Knowledge retention will be checked in the exercise part via problem assignment. Hand-written answer manuscript to the assignment should be submitted to Moodle in a PDF/JPEG/PNG file form scanned by a camera or a scanner. You must pass the problem assignment during the exercise time.
Learning techniques to be incorporated
Suggestions on Preparation and Review	I will assign exercise problems in the class. You are required to solve and exercise the problems in the class. You are also required to review concepts lectured in this class by referencing text books and discussion with class members to understand the concepts.
Requirements
Grading Method	Final Examination is mandatory. The weight ratio for the credit is Exercise problem (about 30%), Final exam (about 60%). The attendance at the exercise and the submission of answers are mandatory as the class credit unit is given to the pair of lecture and exercise parts. When the final exam was on-lined, the grading will be examined by an extra/final homework report.
Practical Experience
Summary of Practical Experience and Class Contents based on it
Message
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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