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Demystifying Spin 1/2 - Math of Quantum Mechanics

Offered By: Mathemaniac via YouTube

Tags

Quantum Mechanics Courses Mathematics Courses Theoretical Physics Courses Lie Algebras Courses

Course Description

Overview

Explore the intricacies of spin 1/2 particles in quantum mechanics through this 34-minute video lecture. Delve into the true meaning behind the statement "If you rotate a spin 1/2 particle by 360 degrees, it doesn't go back to its original state, rather you need 720 degrees." Examine the concepts of "state" and "rotate" in the context of quantum mechanics, and learn why common demonstrations of spin 1/2 can be misleading. Discover the mathematical construction behind spin 1/2 particles, including the relationship between SU(2) and SO(3) groups. Gain insights into the Bloch sphere visualization method and understand the "spin-1/2 property" from a rigorous mathematical perspective. Challenge common misconceptions about spin-s particles and prepare for potential future discussions on higher spins, Lie groups, algebras, and representations.

Syllabus

Introduction
Chapter 1: "State"
Chapter 2: "Rotate"
Chapter 3: The construction
Chapter 4: The "spin-1/2 property"


Taught by

Mathemaniac

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