2x2 matrices in terms of Pauli matrices

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📚 2x2 matrices are used to represent operators acting on 2-dimensional state spaces such as that of the spin angular momentum of spin 1/2 particles like the electron. In this video, we show that we can write any 2x2 matrix in terms of the identity and Pauli matrices. This provides a convenient language for the description of 2-state quantum systems.

0:00 Introduction
1:27 Pauli matrices
2:09 2x2 matrices in terms of Pauli matrices
10:29 Hermitian 2x2 matrices in terms of Pauli matrices
14:58 Wrap-up

⏮️ BACKGROUND
Pauli matrices:    • The Pauli matrices  
Operators:    • Operators in quantum mechanics  
Matrix formulation:    • Matrix formulation of quantum mechanics  
Hermitian operators:    • Hermitian operators in quantum mechanics  

⏭️ WHAT NEXT?
Two-state quantum systems | Eigenvalues:    • 2-state quantum systems: energy eigen...  
Two-state quantum systems | Eigenstates:    • 2-state quantum systems: energy eigen...  
Spin 1/2: [COMING SOON]
Rabi oscillations: [COMING SOON]

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Director and writer: BM
Producer and designer: MC