Quantum field theory and the hydrogen atom

  • I
  • Thread starter arupel
  • Start date
  • #1
45
2
Quantum mechanics does a good job in describing the hydrogen atom. Are there any views either mathematically or conceptually in describing the hydrogen atom?
 

Answers and Replies

  • #2
Urs Schreiber
Science Advisor
Insights Author
Gold Member
573
672
Could you check if you forgot some words in your question? Your question title suggests that maybe you meant to ask whether quantum field theory has anything to say regarding the hydrogen atom on top of what quantum mechanics has to say?

If so, the answer is Yes! The first such QFT effect on the hydrogen atom is called the Lamb shift.
 
  • Like
Likes vanhees71, bhobba and Demystifier
  • #3
haushofer
Science Advisor
Insights Author
2,522
921
The first calculation you should do in this context (but the question is a bit blurry, as Urs stated) is to calculate the Compton wavelength of the electron in Hydrogen and compare this to the size of the hydrogen atom. This should give you a good understanding why "ordinary" QM is so succesfull in explaining the spectrum of hydrogen.
 
  • #4
dextercioby
Science Advisor
Homework Helper
Insights Author
13,112
663
This is well within Standard Model, nothing beyond. A moderator could move it to the quantum one, if the OP sticks to the title.
 
  • #5
DrClaude
Mentor
7,607
4,009
This is well within Standard Model, nothing beyond. A moderator could move it to the quantum one, if the OP sticks to the title.
Moved.
 
  • #6
45
2
I have a general idea about QFT, but not much more. I see QFT as dealing with fields. I was surprised that a QFT effect is the Lamb shift. Could someone give a general basic description how this works.

Thanks,
Arthur Rupel

PS I thought QM had one up on QFT. Evidently I was wrong.

Thanks, Arthur Rupel
 
  • #7
Urs Schreiber
Science Advisor
Insights Author
Gold Member
573
672
Could someone give a general basic description how this works.

The Lamb shift is a tiny shift in the energy spectrum of excitations of the electron orbits in the hydrogen atom.

LambShift.png


This is a “fine structure” effect not seen by the quantum mechanics of the electron, but resulting from radiative corrections involving photon emission/absorption only seen by regarding the electron in perturbative quantum field theory, here in quantum electrodynamics.

The Lamb shift may be attributed to 1-loop Feynman diagrams contributions giving “radiative corrections” to the basic tree level vertex that describes the basic interaction of the electron with the background electromagnetic field, hence called vertex corrections.

LambShiftVertexCorrections.png


(Here the dot on the right is the external vertex for the background electromagnetic field.)

The main contribution (often referred to as the vertex correction) is due to the radiative correction induced by the electron emitting a virtual photon, then interacting with the background electromagnetic field, and and re-absorbing the virtual photon; described by this Feynman diagram:

LambShiftMainVertexCorrection.png


Historically, the observation of the Lamb shift in experiment catalyzed the theoretic development of quantum electrodynamics specifically and of perturbative quantum field theory generally.
 

Attachments

  • LambShift.png
    LambShift.png
    82.1 KB · Views: 710
  • LambShiftVertexCorrections.png
    LambShiftVertexCorrections.png
    19 KB · Views: 691
  • LambShiftMainVertexCorrection.png
    LambShiftMainVertexCorrection.png
    2.1 KB · Views: 578
Last edited:
  • Like
Likes vanhees71, dextercioby and DrClaude
  • #8
45
2
Thanks.
 

Related Threads on Quantum field theory and the hydrogen atom

  • Last Post
Replies
2
Views
3K
Replies
3
Views
856
Replies
1
Views
5K
  • Last Post
Replies
0
Views
2K
Replies
1
Views
6K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
8
Views
2K
Replies
5
Views
3K
Replies
1
Views
459
Top