I have just started to study quantum mechanics, so I have some doubts.(adsbygoogle = window.adsbygoogle || []).push({});

1) if I consider the base given by the eigenstates of s_z [tex]s_z | \pm >=\pm \frac{\hbar}{2} |\pm>[/tex] the spin operators are represented by the matrices

[tex]s_x= \frac {\hbar}{2} (|+><-|+|-><+|)[/tex]

[tex]s_y= i \frac {\hbar}{2}(|-><+|-|+><-|)[/tex]

[tex]s_z=\frac{\hbar}{2}(|+><+|-|-><-|)[/tex]

but I don't have clear idea of what they correspond to concretely. Considering the Dirac formalism, can they be represented by Pauli's matrices?

[tex]s_x=\frac {\hbar}{2} \sigma_x; s_y= i \frac {\hbar}{2} \sigma_y; s_z=\frac {\hbar}{2} \sigma_z[/tex]

2) I can write a vector using its components, e.g. v=(a,b)

but which are the components of the eigenstates of s_z?

3) If I have a state such as [tex]s_x |\phi>=\frac {\hbar}{2} |\phi> [/tex]

and I want to write it using the base of the eigenstates of s_z,

can I write [tex] |\phi>=a|+>+b|->[/tex], with [tex]|a|^2+|b|^2=1?[/tex] (I need this condition to have a normalized vector)

Is it equal to [tex]\frac {e^{i\theta}}{\sqrt 2}(|+>+|->)?[/tex]

Many thanks for your help!

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Representation of spin matrices

Loading...

Similar Threads - Representation spin matrices | Date |
---|---|

B Gravity and spin 2 representation | Jan 6, 2018 |

Projective representations of the spin group | Apr 24, 2014 |

Matrix representation of spin | Jan 26, 2013 |

How does spin work in the position representation? | Apr 14, 2012 |

**Physics Forums - The Fusion of Science and Community**