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- Common courses
- Liberal arts and basic science courses
- Academic unit or major
- Undergraduate major in Physics
- Instructor(s)
- Matsushita Michio Takahashi Kazutaka Nasu Joji
- Class Format
- Lecture / Exercise
- Media-enhanced courses
- Day/Period(Room No.)
- Mon5-6(H112) Mon7-8(W621,W631) Thr5-6(H112)
- Group
- -
- Course number
- PHY.Q311
- Credits
- 3
- Academic year
- 2018
- Offered quarter
- 3Q
- Syllabus updated
- 2018/10/10
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
-
Course description and aims
The lecture start with scattering of a paarticle in the central-force field. Then, two topics follow to show quantum mechanical formalism is not limited to only one. The second topics of the lecture is second quantization developed for many-body systems ofidenticcal particles and the third is density natrix method, which can handle not only pure quantum states but also statistical mis state of them.
Student learning outcomes
One will become able to explain
(1) scattering by central force is a one-dimensional problem.
(2) formalism of field quantization using creation annihiration operaators.
(3) time evolution of a two-level system is represented by the motion of Bloch vector.
Keywords
scattering, Born approximation, phase shift, Boson, Fermion, second quantization, density matrix
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
The lecture will present the concepts that led to variants of formalism within the framework of quantum tgory. The exercise will provide essential examples.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Photon, electron wave, and wave equation | Overview of the lecture will be presented. |
| Class 2 | Symmetry, coordinate transformation, and separation of variables | Explain that a proper choice of the coordinate system often simplifies a complex multi-dimensional problem by separation of variables. |
| Class 3 | Quantum theory of scattering | Explain that a scattering process can be regarded as a steady state of a particle in a central force field. |
| Class 4 | Integral equation of scattering and Born approximation | Explain the derivation of the integral equation of scatttering from Schroedinger equation for a stationary state of a scattering particle. |
| Class 5 | Partial wave expansion and phase shift | Explain that calculation of scattering is simpler if the wavefunction of the particle is expanded by spherical harmonic functions. |
| Class 6 | Rutherford scattering | Explain that Coulombic scattering shows specific features due to its weak distance-dependence. |
| Class 7 | Identical particles | Explain that using creation and annihiration operators, quantum state of many-body system of idedntical particles can be formulated in terms of particle numbers. |
| Class 8 | Field operator | Explain second quantization of Hamiltonian by field operators. |
| Class 9 | Many electron system | Explain Hartree-Fock approximation, the basic approximation of many-electron system. |
| Class 10 | Quantization of electromagnetic field | Explain the procedure of quantization of the free radiation field. |
| Class 11 | Coherent light | Explain properties of coherent state in comparison with photon-number state. |
| Class 12 | Density matrix | Explain that the density matrix describes of nonpure stateas. |
| Class 13 | Liouville operator | Explain that the time evolution of the density matrix is governed by its commmutation relation with Hamiltonian. |
| Class 14 | Bloch equation | Explain two different relaxation proceses introduced to Bloch quation . |
| Class 15 | Rabi oscilation and adiabatic passage | Explain that two-level sytem strongly interacting with light shows Rabi oscillation. |
Textbook(s)
None specified.
Reference books, course materials, etc.
Provided during class.
Assessment criteria and methods
Evaluated by a final exam.
Related courses
- PHY.Q207 ： Introduction to Quantum Mechanics
- PHY.Q208 ： Quantum Mechanics II
- PHY.Q206 ： Analytical Mechanics
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Introduction to Quantum Mechanics and Quantum Mechanics II are prerequisite.
Contact information (e-mail and phone) Notice : Please replace from "[at]" to "@"(half-width character).
matsushita[at]phys.titech.ac.jp
