Question

For the three matrices given below, which one of the choices is correct?

• A. \( \sigma_1 \sigma_2 = -i \sigma_3 \)
• B. \( \sigma_1 \sigma_2 = i \sigma_3 \)
• C. \( \sigma_1 \sigma_2 + \sigma_2 \sigma_1 = I \)
• D. \( \sigma_3 \sigma_2 = -i \sigma_1 \)

Hint:

The Pauli matrices obey specific multiplication rules, and understanding their commutation relations is essential for problems in quantum mechanics.

Answer 1

The Correct Option is B

Step 1: Understanding the Pauli matrices.
The Pauli matrices \( \sigma_1, \sigma_2, \sigma_3 \) are the fundamental matrices in quantum mechanics used to describe spin and related quantities. They follow specific commutation relations. We can compute the product \( \sigma_1 \sigma_2 \) using matrix multiplication. The result is \( i \sigma_3 \), which matches option (B).
Step 2: Conclusion.
Thus, the correct answer is option (B), as the product \( \sigma_1 \sigma_2 = i \sigma_3 \).