Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Hydrogen Atom in homogeneous magnetic vector potential

  1. Jun 7, 2014 #1

    VVS

    User Avatar

    Hey!

    I did an quantum mechanical analysis of a Hydrogen Atom in a homogeneous magnetic vector potential (I know that it might be impossible to create this kind of field) out of curiousity. I showed it to some professors of mine, but they all said that they don't have time. So I decided to post it online here for checkup.

    Here is the analysis View attachment Hydrogen_in_Vector_Potentialv2.pdf

    And here is a short appendix about the evaluation of the derivatives of Spherical Harmonics.
    https://www.physicsforums.com/attachment.php?attachmentid=67418&d=1394285330

    I would really appreciate it if you guys could have a look at the analysis and point out mistakes if there are any.

    thanking you in advance
    VVS
     
  2. jcsd
  3. Jun 7, 2014 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    What is the result?

    I would be surprised to see any deviation from the regular hydrogen atom, as homogeneous vector potentials should be covered by gauge invariance.
     
  4. Jun 7, 2014 #3

    VVS

    User Avatar

    Hey mfb!
    I get a very weird result. Using perturbation theory you get imaginary corrections terms for the energy eigenvalues. That is as far as I know possible. But it basically means that the wave function decays to zero. But I am more concerned with the rate at which it decays, which according to the equations is VERY VERY FAST.
    Something must be wrong.
    VVS
     
  5. Jun 8, 2014 #4

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Or your perturbation theory does not give proper results.

    Indeed, as the result is clear: there is no deviation. The wavefunction might get phase changes, but the energy eigenvalues stay the same.
     
  6. Jun 8, 2014 #5

    VVS

    User Avatar

    I am not satisfied with that answer. Go through the calculations before you make any judgement or show me a different proof.
     
  7. Jun 8, 2014 #6

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    I found a way to get the result without any calculations. Isn't that much more elegant?
     
  8. Jun 8, 2014 #7

    Vanadium 50

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor

    Here's a second calculation: if A is constant, B = 0. If B is zero, there's no Zeeman effect, so you get the same energy levels as a hydrogen atom in vacuum.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Hydrogen Atom in homogeneous magnetic vector potential
  1. Hydrogen atom (Replies: 3)

Loading...