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mfb

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Where do you see a magnetic field? The electron "moves"*, but the nucleus does not (if you reduced the 2-body problem to a 1-body 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

"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

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http://en.wikipedia.org/wiki/Zeeman_effect

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Dont they have something like this in E&M?

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mfb

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In quantum field theory, there is some sort of self-interaction, but that cannot be explained with a classical electromagnetic field.

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http://books.google.co.in/books?id=8qHCZjJHRUgC&pg=PA747&dq=radiation+reaction+jackson&hl=en#v=onepage&q=radiation%20reaction%20jackson&f=false

where it is stated that only for time greater than τ which is of the order of 10

,radiative effects become important.it is only important when motion changes suddenly in that much time which is of course not the case.

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Jano L.

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Only if the particle was extended in space. Then one part of the particle could move in the field of another part. However, there is not much evidence for such structured electron and it is difficult even to formulate such theory consistently, so most usually electrons are assumed as points, both in classical electrodynamics and in quantum theory.

Dont they have something like this in E&M?

Because the Hamiltonian description is well suited for forces which are given by values of r and p. Radiation reaction force [itex]k\dot \mathbf{a}[/itex] does not fit into this framework - it contains second derivative of momentum.When I write down the Hamiltonian for the hydrogen atom why do we not include a radiation term or a radiation reaction term?

If it is external magnetic field (due to magnet), then one can include it via vector potential or terms like [itex]-\boldsymbol{\mu}\cdot\mathbf B[/itex] into the Hamiltonian. However, there is not much reason to include self-interaction of electron with its own field in the Hamiltonian. For example, most quantum-chemical calculations never use such terms and give quite good results (see Slater, Solid State and Molecular Theory: A Scientific Biography).If I had an electron moving in a B field it seems like I would need to have these terms included.

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Jano L.

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[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.

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for hydrogen atom the only time parameter we can see is of order of10

http://books.google.co.in/books?id=8qHCZjJHRUgC&pg=PA747&dq=radiation+reaction+jackson&hl=en#v=onepage&q=radiation%20reaction%20jackson&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.

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mfb

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This shows that radiative corrections are small.It is of order of 10^{-17},which is far from 10^{-24}.

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