2024 Quantum Mechanics II(Lecture)

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Academic unit or major
Undergraduate major in Physics
Nishida Yusuke 
Class Format
Media-enhanced courses
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Syllabus updated
Lecture notes updated
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Course description and aims

This course covers quantum mechanical treatment of the following topics.
* particle motion in central force
* charged particles in background magnetic field
* variational and perturbation theory

Student learning outcomes

At the end of this course, students will understand the Schroedinger equation in the three-dimensional space, and will be able to explain the energy spectrum of a hydrogen atom and apply variational and perturbative methods.


Schroedinger equation, angular momentum, spin, hydrogen atom, Zeeman effect, fine structure, perturbation, variational methods

Competencies that will be developed

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

Class flow

Lectures with blackboard

Course schedule/Required learning

  Course schedule Required learning
Class 1 Schroedinger equation in thee-dimensional space Understand a derivation of the energy spectrum of a particle in a box.
Class 2 spherical harmonics Separate out the angular variables and drive spherical harmonics.
Class 3 angular momentum Understand the definition of the angular momentum and the commutation relations among its components.
Class 4 wave equation for radial direction Understand the energy spectrum of a particle in a spherical square well potential.
Class 5 hydrogen atom Derive the energy spectrum of a hydrogen atom.
Class 6 angular momentum algebra Construct the eigenstates from the commutation relations.
Class 7 spin Understand the similarity and the difference between spin and orbital angular momentum.
Class 8 product of angular momenta Explain the product of two angular momenta.
Class 9 motions in electromagnetic fields Understand the interaction between charged particles and background electromagnetic fields.
Class 10 fine structure Explain the fine structures of hydrogen atom.
Class 11 time independent perturbation theory for nondegenerate case Apply the time independent perturbation theory for nondegenerate systems.
Class 12 time independent perturbation theory for degenerate case Apply the time independent perturbation theory for degenerate systems.
Class 13 time dependent perturbation theory Apply the time dependent perturbation theory.
Class 14 variational method Apply the variational method.

Out-of-Class Study Time (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 by referring to textbooks and other course material.


Lecture notes will be distributed via T2SCHOLA.

Reference books, course materials, etc.

Textbooks specified by the instructor.

Assessment criteria and methods

Evaluation based on reports and the final exam

Related courses

  • PHY.Q207 : Introduction to Quantum Mechanics
  • PHY.Q218 : Quantum Mechanics II(Exercise)

Prerequisites (i.e., required knowledge, skills, courses, etc.)

Students should have completed Introduction to Quantum Mechanics

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