# B Interaction between a neutral atom and an external magnetic field

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1. Apr 3, 2017

### davidt92

Lets suppose that I have a magnetic dipole moment at (0,0,0) pointing to the Z axis, and in the position (X,Y,Z) in the space, I have a Hydrogen atom, I would like to know the exact interaction between the magnetic field created by the magnetic dipole moment in (0,0,0) and the magnetic fields of the atom (spin of the only electron that hydrogen atom have, and the magnetic field created for the rotation of the electron along the nucleus, Larmor precession, magnetic quantum number...), I have some concepts but i don't know how to relate all.

What i have:

For the moment, I have found a system of second order differential equations, solved using the Runge-Kutta method, In this system, I have a magnetic dipole moment at (0,0,0) pointing throw z-axis and i put another dipole also with the magnetic pointing throw z direction and with an initial position (X0,Y0,Z0) and initial velocity (Vx(0),Vy(0),Vz(0)) , also I give to this last spin freedom of movement but its magnetic moment always point up, I also ignore coulomb repulsion forces, the equation give me the position and the velocity of this dipole at any given time t>0 (I'm new here and I don't know how to put formulas, but as i've said is a system of 3 second order diferential equations: d^2(x(t))/dt^2=f(x,y,z,t), d^2(y(t))/dt^2=g(x,y,z,t), d^2(z(t))/dt^2=h(x,y,z,t) ).

What I want to achieve: I want to create a simulation where I can put some molecule, and see his behaviour over time in a inhomogeneous magnetic field.

For the moment only consider a hydrogen molecule, because with big molecules the spins will have some coupling effects that for the moment I would like to ignore.

In conclusion, I would like to know the force that produce and external magnetic field with the intrinsic magnetic field of an hydrogen atom taking in account all the effects that this external (and inhomogeneous) magnetic field could affect to the position (X,Y,Z) of the atom and the direction of its magnetic dipole moment

Last edited: Apr 3, 2017
2. Apr 8, 2017

### PF_Help_Bot

Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.

3. Apr 11, 2017

### Khashishi

Is the distance between the dipole and hydrogen atom large compared to the dimensions of the hydrogen atom? If so, then you can approximate the field as constant over the volume of the hydrogen atom then use the Zeeman effect to calculate the effect on the atom's energy levels. You'll probably want to choose coordinate system such that the spin is parallel or antiparallel to the magnetic field at the center of the atom. Then you can set up a Hamiltonian something like this:
$H=\frac{p_H^2}{2m_H} + E_H + \frac{p_d^2}{2m_d}$
where $p_H$ is the momentum of the hydrogen atom, $E_H$ is the energy of the hydrogen atom (calculated from the Zeeman effect), $p_d$ is the momentum of the dipole. Maybe you have rotational energy of the dipole also. It's not clear if you are talking about a classical dipole or something quantum (described by a spinor).

4. Apr 12, 2017

### davidt92

Thank you very much, I think I have to consider both (Classical and quantum), the classical part will be the behavour of my hydrogen atom inside the magnetic field. the quantum part will be how this hydrogen atom express his magnetic dipole moment in space