# Quantum Mechanics I

Lecturer Masaharu TANABASHI, Professor School of Science / Graduate School of Science, 2017 Fall Department of physics

### Course Features

In order to be able to apply quantum mechanics, there are 2 obstacles we must overcome. The first obstacle is the introduction of a new, unfamiliar concept. At the core of quantum mechanics, lies concepts that are manifested but rarely experienced in everyday life, such as "Quantum superposition of states", and "Physical quantity corresponding to an operator", etc. The second obstacle is the problem of mathematical techniques and skills. In quantum mechanics, we do not only use new and recent concepts, but also by utilizing skills and techniques we have just learned, we can at last, for the first time understand and confirm the reasoning behind certain experiment results.

In this lecture, I will distribute lecture notes to students beforehand so that as many students as possible can overcome the aforementioned obstacles. Moreover, by combining the lectures with tutorial classes, I will prepare some practice questions related to the lecture. By distributing the lecture notes, the students will be freed from the necessity to take notes so they can focus their attention on learning new concepts. Furthermore, since the distributed lecture notes can be used for the preparation and the revision of lectures, students can try the practice problems from the tutorial, and also solve conceptual problems taught in class. Therefore I expect the students to then apply the newly learned mathematical techniques to solve problems about quantum mechanics.

### Course Aim

We aim to achieve a substantial understanding of the fundamental concepts of quantum mechanics, which are necessary throughout many fields of modern physics. We shall cultivate critical thinking skills by understanding the framework of quantum mechanics, which differs greatly from the classical mechanics that you are used to. To be specific, first, by solving problems in one-dimension, we shall study the quantum mechanical 'state',
'operators' that act on states, and their relation to measurable physical quantities. Next, we shall take up three-dimensional central force problems, and study the quantum mechanics of the Hydrogen atom.

### Course Content

1. Introduction
2. Wave-particle duality, probability, the Schroedinger equation
3. Eigenvalues, eigenfunctions, expansion of the wave function in terms of eigenfunctions
4. One-dimensional potentials
5. The structure of quantum mechanics
6. Operator methods
7. Angular momentum
8. The Hydrogen atom

### Learning Objectives

To understand the basic solution methods of the Schroedinger equation, the probability interpretation of the wave function, and properties of operators.

### Textbook

S. Gasiorowicz, "Quantum Physics", 3rd edition, John Wiley & Sons Pub.

Mostly based on performance in regular exams

Course withdrawal, failing grade (F) and criteria for an absent grade Withdrawal from the course is not possible. Students absent from exams without prior notice shall be given the ABSENT grade for the entire course. Students who fail both the regular exams and the retests shall be given the FAIL grade.

#### Last updated

March 17, 2020

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