Hey,(adsbygoogle = window.adsbygoogle || []).push({});

I just have a quick question that I haven't quite been able to find a definitive answer to, regarding conjugate momenta in the Hamiltonian.

Ok, so it regards the following term for the hamiltonian in a magnetic field:

[tex]H=\frac{1}{2m}(p-qA)^2 [/tex]

I'd like to ask whether [tex]p[/tex] is the conjugate momentum or if [tex]p_c=p-qA[/tex] is the conjugate momentum. As a guess, I would say that [tex]p_c=p-qA[/tex] is the conjugate momentum, as it seems to me that the hamiltonian should take into account the magnetic field. Would this then mean that the hamiltonian could be written as [tex]H=\frac{1}{2m}(p_c)^2 [/tex]

Also, very important, does [tex] -i\hbar\nabla[/tex] represent the canonical momentum operator or the classical/mechanical momentum operatpor?

Im sure the answers are around somewhere on the internet, but it strikes me that there are some conflicting statements and a tendency to just go "oh yeah, now we swap the canonical momentum, [tex]p[/tex] for mechanical momentum [tex]p[/tex]" and the like, so it would be nice to get a definitive answer.

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!

# Conjugate momentum in the hamiltonian

Loading...

Similar Threads - Conjugate momentum hamiltonian | Date |
---|---|

A Hermitian conjugate of the derivative of a wave function | Feb 21, 2018 |

I Hilbert space and conjugate of a wave function | Dec 21, 2017 |

I Fourier conjugates and momentum | Oct 3, 2017 |

I What is the complex conjugate of the momentum operator? | Apr 30, 2016 |

Representation of conjugate momentum | Oct 9, 2015 |

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