2x2 matrices in terms of Pauli matrices
📚 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 eigenvalues
Two-state quantum systems | Eigenstates: • 2-state quantum systems: energy eigenstates
Spin 1/2: [COMING SOON]
Rabi oscillations: [COMING SOON]
~
Director and writer: BM
Producer and designer: MC