- #1

- 488

- 4

[tex]\vec{\sigma} = \sigma_1 \hat{x} + \sigma_2\hat{y} + \sigma_3\hat{z}[/tex]

But each component, [tex]\sigma_i, i=1,2,3[/tex] is a 2x2 matrix. I am really confuse about the relation between [tex]\sigma_i[/tex] and the component of the spin (I mean the magnetic moment) along each cartesian coordinate. For example, why people use [tex]\sigma_2[/tex] to refer to a spin along y direction while [tex]\sigma_2[/tex] is a 2x2 matrix instead of a column/row vector?