2023 Students Enrolled in or before 2015 School of Science Physics

Quantum Mechanics III

Academic unit or major: Physics
Instructor(s): Takehito Yokoyama
Class Format: Lecture (Face-to-face)
Media-enhanced courses: -
Day of week/Period (Classrooms): 5-6 Mon (M-110(H112)) / 5-6 Thu (M-110(H112))
Class: -
Course Code: ZUB.Q313
Number of credits: 200
Course offered: 2023
Offered quarter: 3Q
Syllabus updated: Jul 8, 2025
Language: Japanese

Syllabus

Course overview and goals

This course covers fundamentals and applications of quantum mechanics.We first study the basic methods and the concept for quantum many-body systems, the second quantization and field operators both for bosons and fermions. Next, we study the variational methods used for complex systems. Finally, we study the perturbation theory for stationary systems and for he time-dependent systems.

Course description and aims

(1) Understand field quantization and work with particle creation and annihilation processes in many-body systems
(2) Understand the difference and the characteristics of several trial functions in the variational methods for Fermions.
(3) Calculate corrections of energy levels and states of a system with the method of perturbation

Keywords

identical particles, second quantization, creation operator, annihilation operator, variational method, perturbation

Competencies

Specialist skills
Intercultural skills
Communication skills
Critical thinking skills
Practical and/or problem-solving skills

Class flow

Mostly the blackboard is used to explain the details of the mathematical derivations. At the same time the emphasis is put on the insight into the physical aspects of the system in order to achieve the deep understanding of the quantum mechanics.

Course schedule/Objectives

	Course schedule	Objectives
Class 1	Overview of this lecture Hamiltonian for many-particle systems	Understand the overview of the lecture, and learn the Hamiltonian operator of the many-particle systems
Class 2	Fermions and Bosons	Understand the statistical characteristics of the wavefunctions for fermions and bosons
Class 3	symmetrized products for bosons	Understand the symmetrized products and the matrix elements of the one-particle and two-particle operators between the symmetrized products
Class 4	creation and annihilation operators and the Hamiltonian	Introduce the Hilbert space where the occupation numbers play the independent variables, and also the creation and annihilation operators defined in the spade. Also understand the Hamiltonian written with those operators.
Class 5	field operators and second quantization	Introduce field operators and understand that they give a beautiful and concise Hamiltonian expression.
Class 6	anti-symmetrized products for fermions	Understand the anti-symmetrized products and the matrix elements of the one-particle and two-particle operators between the anti-symmetrized products
Class 7	field operators and second quantization for fermions	Understand the field operators for fermions, their differences from those for bosons, and the second quantization for fermions
Class 8	variational principle in quantum mechanics, and variational methods and trial functions.	Understand the variational principle, and the variational method and trial functions
Class 9	Hartree approximation and Hartree-Fock approximation	Understand the basic but important approximations, Haree and Hartree-Fock approximations
Class 10	Perturbation theory and first-order perturbation	Understand the concept of the perturbation theory in quantum mechanics, and the first-order perturbation theory
Class 11	Second order perturbation theory	Understand the second-order perturbation theory
Class 12	applications of the perturbation theory	Understand the perturbation theory applied to the harmonic oscillator
Class 13	perturbation theory for degenerated systems	Understand how to apply the perturbation theory to the systems with the degenerary
Class 14	time-dependent perturbation theory	Understand the perturbation theory with time-dependent perturbation potential
Class 15	Transition probabilities and Fermi's golden rule Summary	Understand the transition probabilities and the Fermi's golden rule. Summary of the lecture.

Study advice (preparation and review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.

Textbook(s)

Not specified

Reference books, course materials, etc.

"Quantum Theory of Many-Particle Systems" (A. L. Fetter and J. D. Walecka)
"Quantum Mechanics" (L. D. Landau and E. M. Lifshitz)

Evaluation methods and criteria

Examination

Related courses

ZUB.Q204 ： Quantum Mechanics I
ZUB.Q206 ： Quantum Mechanics II
ZUB.S310 ： Thermodynamics and Statistical Mechanics II

Prerequisites

Quantum Mechanics I and II