Calculating SPIN MATRICES for an electron: Sz - Tutorial series on Spin [Part 5]

Описание: In this video, I layout the procedure for finding the matrices corresponding to spin operators specific to an electron (spin-1/2). The procedure can be generalized straightforwardly to an arbitrary non-zero quantum spin. The video explains, why this kind of non-relativistic analysis is not self sufficient, and the particular piece of information regarding the Hilbert space dimension has to be incorporated in an adhoc manner. In this video, I take this information from the experimentally observed eigenvalues for the spin of electron, namely +\hbar /2 and -\hbar /2.

I then proceed to give a very detailed calculation for the matrix elements of the z-component of spin operator (S_z) for an electron. I also stress how this matrix form depends on the structure of the basis vectors |s,m_s), which is an important point.

In the next tutorial, I continue this video and calculate the matrix elements for S^2 (S), S_x and S_y matrices for an electron.

Pre-requisites: Basic knowledge of Quantum Physics and the previous lectures of this series.

Previous Lecture [Part 4] :    • EIGENSTATES and EIGENVALUES of SPIN OPERAT...  
Next Lecture [Part 6] :    • Calculating SPIN MATRICES for an electron:...  

Timestamps:

00:00 Introduction

Who am I?
I'm Priyanshi Bhasin, a PhD candidate at the Indian Institute of Science (IISc).

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