Quantum Chemistry Mehdi Irani

This course introduces the fundamental principles of quantum chemistry, offering a foundation for understanding the atomic and molecular properties that cannot be explained by classical physics. Many students are already familiar with concepts such as atomic orbitals and molecular vibrations, but often without a clear justification. In this course, we aim to build those justifications using quantum mechanics.

Topics covered include the Schrödinger equation, model quantum systems (particle in a box, harmonic oscillator, hydrogen atom), quantum operators, and atomic/molecular structure. Emphasis is placed on both theoretical understanding and problem-solving.

Course Structure

Part I: Foundations of Quantum Chemistry

Historical Background of Quantum Mechanics

The Uncertainty Principle

The Time-Dependent Schrödinger Equation

The Time-Independent Schrödinger Equation

Part II: The Particle in a Box

One-Dimensional Particle in a Box

The Free Particle

Three-Dimensional Box Model

Part III: The Harmonic Oscillator

One-Dimensional Harmonic Oscillator

Molecular Vibrations

Part IV: The Hydrogen Atom

Central-Force Problems

Reduction of Two-Particle Problems

Hydrogen Atom and Hydrogen-Like Orbitals

The Zeeman Effect

Course Material

Textbook:
Quantum Chemistry, 6th Edition, by Ira N. Levine, Prentice-Hall, 2009

Resources:
Shared Google Drive Folder

Weekly Schedule
Session	Topics
1	Overview of Quantum Mechanics (Slides)
2	Historical Background (Sec. 1.2)
3	Time-Dependent Schrödinger Equation (Sec. 1.4) Time-Independent Schrödinger Equation (Sec. 1.5)
4	Probability (Sec. 1.6) Complex Numbers (Sec. 1.7) Units (Sec. 1.8)
5	Problem Solving – Chapter 1
6	Differential Equations (Sec. 2.1) Particle in a 1D Box (Sec. 2.2)
7	Free Particle (Sec. 2.3) Rectangular Box (Sec. 2.4)
8	Problem Solving – Chapter 2
9	Operators (Sec. 3.1) Eigenfunctions & Eigenvalues (Sec. 3.2)
10	Operators & Quantum Mechanics (Sec. 3.3) 3D Many-Particle Schrödinger Equation (Sec. 3.4)
11	3D Particle in a Box (Sec. 3.5) Degeneracy (Sec. 3.6)
12	Expectation Values (Sec. 3.7)
13	Requirements for Acceptable Wavefunctions (Sec. 3.8)
14	Problem Solving – Chapter 3
15	Midterm Exam 1
16	Power-Series Solutions (Sec. 4.1)
17	Harmonic Oscillator (Sec. 4.2)
18	Molecular Vibrations (Sec. 4.3)
19	Problem Solving – Chapter 4
20	Midterm Exam 2
21	Simultaneous Properties (Sec. 5.1) Vectors (Sec. 5.2)
22	Angular Momentum (Sec. 5.3)
23	Ladder Operators (Sec. 5.4)
24	Problem Solving – Chapter 5
25	Central-Force Problem (Sec. 6.1) Separation of Variables (Sec. 6.2)
26	Two-Particle Reduction (Sec. 6.3) Rigid Rotor (Sec. 6.4)
27	The Hydrogen Atom (Sec. 6.5)
28	Hydrogen Atom Wavefunctions (Sec. 6.6)
29	Hydrogen-like Orbitals (Sec. 6.7)
30	Problem Solving – Chapter 6
For the exact date and time of each session, please refer to your Golestan schedule.

Quantum Chemistry (B.Sc. Course)