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Hamiltonian for hydrogen atom? 
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#1
Dec1012, 03:41 AM

P: 2,466

When I write down the Hamiltonian for the hydrogen atom why do we not include a radiation term or a radiation reaction term? If I had an electron moving in a B field it seems like I would need to have these terms included.



#2
Dec1012, 10:52 AM

Mentor
P: 11,900

Where do you see a magnetic field? The electron "moves"*, but the nucleus does not (if you reduced the 2body problem to a 1body problem).
"Classical" quantum mechanics (no quantum field theory) cannot include couplings to external radiation, or has to use effective models for that, so this is neglected in the derivation. Edit: *well, not really, but at least it has a wave function which has expressions similar to a velocity 


#3
Dec1012, 11:43 AM

P: 149

Generally, to begin with, the external magnetic field is ignored. You can add a magnetic field which interacts with the magnetic moment of the atom. This gives rise to the Zeeman effect, the splitting of energy levels based on the zcomponent of the total angular momentum (usually denoted m).
http://en.wikipedia.org/wiki/Zeeman_effect 


#4
Dec1112, 06:04 AM

P: 2,466

Hamiltonian for hydrogen atom?
I was just thinking that the electron was moving into its own B field that it created.
Dont they have something like this in E&M? 


#5
Dec1112, 06:13 AM

Mentor
P: 11,900

No, you don't get this.
In quantum field theory, there is some sort of selfinteraction, but that cannot be explained with a classical electromagnetic field. 


#6
Dec1112, 07:10 AM

P: 1,020

see the page 747 from jackson,here
http://books.google.co.in/books?id=8...ackson&f=false where it is stated that only for time greater than τ which is of the order of 10^{24} ,radiative effects become important.it is only important when motion changes suddenly in that much time which is of course not the case. 


#7
Dec1112, 08:11 AM

PF Gold
P: 1,165




#8
Dec1112, 09:08 AM

P: 2,466

ok thanks for all of your responses. If I had a relativistic electron moving in a B field would I then have a radiation term? The electron is a free particle moving through an external B field.



#9
Dec1112, 09:15 AM

PF Gold
P: 1,165

In relativistic theory, for electron in external magnetic field, I would use
[tex] H = \sqrt{(\mathbf p  \frac{q}{c}\mathbf A)^2c^2 + m^2c^4} [/tex] with [itex]\mathbf A[/itex] such that give the magnetic field in question. 


#10
Dec1212, 12:23 AM

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#11
Dec1212, 09:00 AM

Mentor
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#12
Dec1312, 12:15 AM

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