Spin 1/2 and Pauli Matrices

In this video, I have used the abstract eigenvalue relations we came up with in previous videos to find the matrix representation of spin angular momentum which are formed using 2 by 2 matrices called Pauli matrices. We find the eigenvalues and eigenstates (spinors) of different components of spin angular momentum operator using Pauli matrices and also for an arbitrary direction r(hat). To understand how we came up with the abstract eigenvalue relations for raising and lowering operators and also z component and total spin squared, watch this video: https://youtu.be/59_HZp-sDbo 00:00 Why spin is a purely quantum phenomenon 02:11 What we need to know about spin angular momentum 04:30 The common case of spin 1/2 06:10 Matrix representation of spin angular momentum 08:57 Pauli matrices 14:28 Eigenstates and eigenvalues of spin along x and y directions 17:27 Eigenvalues and Eigenstates of spin along an arbitrary direction