EIGENSTATES and EIGENVALUES of SPIN OPERATORS in an ABSTRACT sense -Tutorial series on Spin [Part 4]

In this video, I fix the Hilbert space for the quantum spin degree of freedom by developing the form of its eigenstates and eigenvalues in an abstract sense. I approach this by writing the commutation relations for the spin operators and a discussion motivated by the orbital angular momentum analysis. I explain why spin can take half integer values as well, in contrast to the integer values for orbital angular momentum. The video also stresses why spin eigenstates come with two labels s and m_s, and explains how to determine the dimension of the Hilbert space in which spin lies. In the end, I apply these concepts to a specific case of spin 3/2 particle, which gives a nice understanding of the spin Hilbert space. Pre-requisites: Basic knowledge of Quantum Physics and the previous lectures of this series. You can find the previous lecture here [Part 3] :    • Why are SPIN OPERATORS in the form of MATR...   Next lecture [Part 5]:    • 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). Follow me on: FB Page:   / bragitoff   FB Page2:   / physwhizforum   IG:   / ___physwhiz___   BLOG: http://bragitoff.com FORUM: http://physwhiz.bragitoff.com #QuantumPhysics #Spin #Eigenvectors #Eigenvalues