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cragar
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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.
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.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?
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.
for hydrogen atom the only time parameter we can see is of order of10-10/107(bohr radius/velocity).velocity is only some approximate idea here.It is of order of 10-17,which is far from 10-24.andrien said:see the page 747 from jackson,here
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.
This shows that radiative corrections are small.andrien said:It is of order of 10-17,which is far from 10-24.
sure,it shows it.the parameter τ is the only parameter in classical electrodynamics which is relevant for considering whether radiative corrections should be included or not.mfb said:This shows that radiative corrections are small.
The Hamiltonian for hydrogen atom is a mathematical operator that represents the total energy of the atom. It includes the kinetic energy of the electron and the potential energy due to its interaction with the nucleus.
The Hamiltonian operator is derived using the principles of quantum mechanics and the Schrödinger equation. It takes into account the mass and charge of the electron and the nucleus, as well as the distance between them.
The Hamiltonian is a crucial component in solving the Schrödinger equation for hydrogen atom. It provides the necessary information about the energy states and wavefunctions of the electron in the atom.
Yes, the Hamiltonian for hydrogen atom can be used to calculate other properties such as the ionization energy, the electron's angular momentum, and the energy levels of the atom. It is a fundamental tool in understanding the behavior of atoms.
The Hamiltonian for hydrogen atom differs from that of other atoms due to the presence of only one electron and one proton. This results in a simpler form of the Hamiltonian, making the hydrogen atom a special case in quantum mechanics.