This is a continuation of “Quantum Mechanics of Materials (MAT.A202.R)”, and is the first of a two course sequence with “Quantum Chemistry B(MAT.P202.E). We begin by reviewing the shortcomings of classical physics and elementary quantum physics. After introducing some useful mathematical tools, we explain the postulates and formulations of quantum mechanics; understanding of operator, physical observable and eigenvalue, commutation relation etc. are developed. The remainder of the course focuses on learning the importance of approximate methods in quantum chemistry and mastering its calculation techniques, such as perturbation and a variation principle. “Quantum Chemistry B (MAT.P202.E)” covers its application to simple real physical systems and is also recommended.
[Outcome] To gain an understanding of advanced materials science, quantum mechanics and the way of its application to chemistry and material engineering are essential in order to answer the questions on the structure and function of materials. Upon successful completion of “Quantum Chemistry A”, students will have accomplished the objectives of learning the approximate methods and techniques in quantum chemistry to apply for real physical systems of materials science and engineering.
[Theme] Quantum mechanics fails to obtain rigorous solutions for complex systems. To overcome these difficulties, many types of approximate methods and techniques have been invented and applied. This course focuses on understanding of perturbation and a variation principle on the basis of elementary quantum mechanics for the application of quantum mechanical calculations.
the Schrödinger Equation, harmonic oscillator, spherically symmetric potential(H-atom), N-particle system, physical observable, eigenvalue, bra-ket notation, commutators, uncertainty principle, physical observable, time evolution of state vectors, conservation, perturbation, variation principle, Ritz method
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | ✔ Practical and/or problem-solving skills |
Course materials are provided beforehand. Before coming to class, students should read the course schedule and contents of the course materials. Required learning should be completed outside of the classroom for preparation and review purposes.
Course schedule | Required learning | |
---|---|---|
Class 1 | Review of elementary quantum mechanics (the Schrödinger Equation) | Homework is given in the class. |
Class 2 | Review of elementary quantum mechanics (Electron as waves, and 1D simple harmonic oscillator) | |
Class 3 | Review of elementary quantum mechanics (Simple rotation, and spherically symmetric potential(H-atom)) | |
Class 4 | Basic Formalism (1) (N-particle system, physical observable and eigenvalues, bra-ket notation) | |
Class 5 | Basic Formalism (2) (commutators and uncertainty principle, physical observable, time evolution of state vectors, and conservation) | |
Class 6 | Approximate method (1) (Perturbation: w/o degeneracy) | |
Class 7 | Approximate method (2) (Perturbation: w/ degeneracy) | |
Class 8 | Approximate method (3) (Variation principle, Ritz method) |
Course materials are provided beforehand
Yoshiya HARADA, "Quantum Chemistry", Sho-kabo, in Japanese
Masayoshi Oiwa, "10 lectures of calculas for chemist", Kagakudojin, in Japanese
Peter ATKINS, Physical Chemistry, Oxford
Homework: 20%, Final Exam: 80%.
It is recommended but not required that before taking quantum chemistry A, students take general physics and calculus, matrix/linear alegra, and ordinary differential and partial equations.