If we define:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]A_{j}=\omega \hat{x}_{j}+i \hat{p}_{j}[/tex]

and

[tex]A^{+}_{j}=\omega \hat{x}_{j}-i \hat{p}_{j}[/tex]

Would it be true to say:

[tex][A_k , (A^{+}_{i}+A_i)(A^{+}_{j}-A_j)]=0[/tex]

My reasoning is that, because

[tex][\hat{x}_{j}, \hat{p}_{i}]=0[/tex]

the the ordering of the contents of commutation bracket shouldn't matter (as [tex]\hat{x}_{j} \hat{p}_{i}=\hat{p}_{i}\hat{x}_{j}[/tex]), so we simply get that:

[tex][A_k , (A^{+}_{i}+A_i)(A^{+}_{j}-A_j)]=A_{k}(A^{+}_{i}+A_i)(A^{+}_{j}-A_j)-(A^{+}_{i}+A_i)(A^{+}_{j}-A_j)A_{k}= A_{k}(A^{+}_{i}+A_i)(A^{+}_{j}-A_j)-A_{k}(A^{+}_{i}+A_i)(A^{+}_{j}-A_j)=0[/tex]

This seems obvious to me, but it would make a 10 mark exam question too easy! Would be grateful if someone could confirm whether this is right or not.

Thanks.

**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!

# Does this commutator commute?

Loading...

Similar Threads - Does commutator commute | Date |
---|---|

I Does a field operator always commute with itself? | Jul 13, 2017 |

Poisson Bracket to Commutator, What Does it REALLY Mean? | Dec 28, 2011 |

How does non-commutativity emerge from path integral? | Dec 31, 2010 |

What does simultaneous reality and non-commuting operators mean? | Nov 15, 2010 |

Does every observable commute with the hamiltonian? | Mar 16, 2008 |

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