量子力學(一)

This is the first semester course of a one year exposition of quantum mechanics in the graduate level. The students are expected to have a background of an undergraduate level introductory course in quantum mechanics. Therefore, the course will not stress upon the experimental basis on the formulating of the Schrodinger equation, but rather, will start right from it to explore issues that involve operators, basis, quantum dynamics (i.e. time evolution of the quantum states), angular momentum, and symmetry in quantum mechanics.

Introduction to Quantum Mechanics I & II.

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Home work & Quizzes (20%) Midterm Exams. (2x25%) Final Exam. (30%)

• Chapter 1: Fundamental concepts

  * The Stern-Gerlach Experiment * Kets, Bras, and Operators * Base Kets and Matrix Representation * Measurements, Observables, and the Uncertainty Relations * Change of Basis * Position, Momentum, and Translation * Wave Functions in Position and Momentum Space

• Chapter 2: Quantum Dynamics

  * Time Evolution and the Schrodinger Equation * The Schrodinger Versus the Heisenberg Picture * Simple Harmonic Oscillator * Schrodinger’s Wave Equation * Propagators and Feynman Path Integrals * Potentials and Gauge Transformations

• Chapter 3: Theory of Angular momentum

  * Rotations and Angular Momentum Commutation Relations * Spin 1/2 Systems and Finite Rotations * O(3), SU(2), and Euler Rotations * Density Operators and Pure Versus Mixed Ensembles * Eigenvalues and Eigenstates of Angular Momentum * Orbital Angular Momentum * Addition of Angular Momenta * Schwinger’s Oscillator Model of Angular Momentum * Spin Correlation Measurements and Bell’s inequality * Tensor Operators

J.J. Sakurai, Jim Napolitano "Modern Quantum Mechanics" Second Edition Pearson

地點

SC 458

時間

Wednesday 4:00~5:00 p.m.

聯絡方式

(Office phone no.: 56127)