## 基本素養 Basic Literacy

□ 具國際宏觀、社會與人文關懷的公民素養。

同理學院能力代碼B、C、D

To appredate the humanitles, cultivating talent with global perspectives, and to express social concern.

□ 邏輯思考、理性判斷、嚴謹確實、合作創新與尊重學術倫理的科學態度。

同理學院代碼E、F、H

with respect to academic ethics and integrity, to equip oneself with a scientific attitude of logical thinking, rational judgement, discipline and practical, cooperation and innovation.

## 核心能力 Competence

■ 基礎物理知識

Basic knowledge of Physics

□ 進階物理知識

advance knowledge of Physics

□ 高階物理知識

Knowledge of Advance Physics

□ 科學實驗、數據分析、與解釋實驗結果的能力

To conduct an experiment, analyze data information and to explain the results of scientific experiments

□ 程式設計與軟體應用的能力

programing capability

## 課程概述 Course Description

本課程為英語授課，請詳英文簡介。Physics is the science of change and of measurement. Change is seen against the changeless and measurement is the process of comparing a property to a well defined and agreed upon referent. Quantum mechanics, as a branch of physics, is primarily a theory of transformations that realize the changes of quantum states and the operators of quantum mechanics are the generators of those transformations. The formulation of the physical laws uses the mathematics of transformations and the important properties appear as the invariants or nearly invariants of the transformations. The issue of measurement lies at the heart of interpretation of quantum theory. In a quantum measurement, the error in an observable and the disturbance in its canonically conjugate observable caused by the measurement, together with the quantum fluctuations, are related and have been formulated as Kennard-Robertson's, Heisenberg's, Schrodinger's, and Ozawa's inequalities. This course embraces the following main topics: Mathematical foundation of quantum mechanics: quantum states and Hilbert spaces, observables and operators, commutation relations and Heisenberg's uncertainty principle, pure and mixed states, density operator; Quantum dynamics: time evolution and the Schrodinger equation, Schrodinger and Heisenberg pictures, interaction or Dirac picture, quantization of harmonic oscillator, potential and gauge transformation; Theory of angular momentum: rotation and angular momentum operator, spin and SU(2) group, orbital angular momentum, solution of the hydrogen atom, addition of angular momenta and Clebsch-Gordan coefficients, tensor operators and Wigner-Eckart theorem; Symmetry in quantum mechanics: conservation laws and degeneracies, parity, time-reversal symmetry.

## 課程學習目標 Course Objectives

## 課程進度 Progress Description

進度說明 Progress Description | |
---|---|

1 | Review of old quantum theory. |

2 | Fundamentals of Hilbert Space: Vector spaces and Hilbert spaces. |

3 | Dirac notation. Self-adjoint and Unitary operators and their spectra. |

4 | Symmetries and unitary transformations. Projection operators |

5 | Time-evolution and Schrodinger's equation. |

6 | Simple Quantum Systems. Simple harmonic Oscillator. |

7 | Measurement, Observables and Uncertainty relation. |

8 | Two-state systems, electron spin |

9 | Mid-exam |

10 | Quantum dynamics: Time evolution operator. |

11 | Heisenberg equations of motion. Heisenberg and Schrodinger representations. Interaction or Dirac representation. |

12 | Symmetry in QM: Symmetries and conservation laws. |

13 | Angular momentum and commutation relations. |

14 | Addition of angular momentum I. |

15 | Addition of angular momentum II. |

16 | Spin Correlation and Bell's Inequility, quantum entanglement |

17 | Identical particle and statistics properties. |

18 | Final Exam. |

以上每週進度教師可依上課情況做適度調整。The schedule may be subject to change.

## 有關課程其他調查 Other Surveys of Courses

1.本課程是否規劃業界教師參與教學或演講? 否Is there any industry specialist invited in this course? How many times? No

2.本課程是否規劃含校外實習(並非參訪)? 否

Are there any internships involved in the course? How many hours? No

3.本課程是否可歸認為學術倫理課程? 否

Is this course recognized as an academic ethics course? In the course how many hours are regarding academic ethics topics? No

4.本課程是否屬進入社區實踐課程?

Is this course recognized as a Community engagement and Service learning course? Which community will be engaged?