Schedule of Classes
-
Lecture: Mon, Wed, Fri. 3:00 PM - 3:50 PM, RWAC 0115
-
Discussion session: Thu. 7:00 PM - 7:50 PM, YORK 4080A
-
Instructor: Yi-Zhuang You (尤亦庄) (sounds like EACH-ONE, YOU) (He/Him/His)
-
Email: yzyou@ucsd.edu
-
Office hours: by schedule, Mayer 5202 or Zoom https://ucsd.zoom.us/my/yzyou
-
- Teaching Assistants: Pathak Parashar. Email: psparash@ucsd.edu
-
Grader: Shuhan Zhang. Email: shz091@ucsd.edu
- Course Grade Allocation:
- Homework: 70%
- Mid-term Exam: 10%
- Final Exam: 20%
- Assignment and Submission Platform:
- Homework and exams are online. They will all be assigned and submitted via the UCSD Canvas platform.
-
Homework Guidelines:
-
Assignments will occur irregularly, depending on when the homework problem is encountered in the lecture.
-
A recommended deadline will be provided for each assignment. However, there are no penalties for late submissions (meaning that submissions are accepted until the end of the quarter). But please kindly manage your submissions to alleviate the TA’s workload.
-
For homework, discussion among students and consulting with the TA are allowed. You may utilize all educational resources (including AI language models). Nevertheless, you are required to complete your assignments by yourself to maintain academic integrity. You are encouraged to acknowledge in your homework the resources that are helpful to you.
-
-
Examination Policies:
-
The scheduling for the mid-term and final exams has yet to be determined. Your input regarding preferred time slots is welcome.
-
Exams will be announced online, and you will typically be given a two-day window for completion. Extensions may be granted under exceptional circumstances.
-
All exams are take-home and open-book in nature. You are permitted to consult textbooks and lecture notes, employ computational tools, browse online resources, and interact with AI language models. However, discussing the exam content with other humans is not allowed.
-
Textbooks
Text books for reference:
[1] Arjun Berera and Luigi Del Debbio, Quantum Mechanics. Cambridge University Press, New York (2021).
[2] Andrew J. Larkoski. Quantum Mechanics – A Mathematical Introduction. Cambridge University Press, New York. (2023)
[3] J. J. Sakurai, Modern Quantum Mechanics. Addison-Wesley Publishing Company. (1994)
[4] R. Shankar, Principles of Quantum Mechanics. Plenum Press, New York. (1994)
Lecture Notes
As a UCSD student, you have free access to Mathematica (see how).
Part 1. Path Integral Quantization (Mathematica) (PDF)
- From Classical to Quantum
- Historical Review
- Quantization of Light
- Path Integral Quantization
- Quantization of Matter
- Deriving the Schrödinger Equation
- Semiclassical Approach
Part 2. Piecewise Potentials (Mathematica) (PDF)
- Basic Piecewise Potentials
- General Setup
- Free Particle (Flat Potential)
- Hard-Wall Potential
- Infinite Square Well
- Step Potential
- Square Potential
- Dirac Potential
- Double Dirac Potential
- Periodic Dirac Potential
- General Piecewise Potentials
- Transfer Matrix Method
- Applications
Part 3. Algebraic Methods (Mathematica) (PDF)
- Introduction
- Functions are Vectors
- Position and Momentum
- Harmonic Oscillator
- Operator Algebra
- Quantum Bootstrap
- Representation Theory
- Angular Momentum
- Operator Algebra
- Quantum Bootstrap
- Representation Theory
- Fusion Category
- Hydrogen Atom
- Background: Classical Mechanics
- SO(4) Symmetry
- Spectrum
Part 4. Perturbation Theory (Mathematica) (PDF)
- Time-Independent Perturbation
- A Toy Model of Qubit
- Non-Degenerate Perturbation Theory
- Degenerate Perturbation Theory
- Time-Dependent Perturbation
- Time-Dependent Perturbation Theory
- Energy Level Transitions
Part 5. Phase and Gauge (Mathematica) (PDF)
- Gauge Principles
- Gauge Structure and Berry Phase
- Gauge Field and Electromagnetism
- Uniform Magnetic Field
- Classical Dynamics
- Landau Level Quantization
- Quantum Hall Effect
- Spin and Monopole
- Classical Spin
- Magnetic Monopole
- Quantum Spin