System of hydrogen atoms in an electric field

[Reid]

Using the first order perturbation theory I will determine the probability of finding some atoms in a certain state. The electric field is directed along the z-axis. But i don't understand how this is done.

Should I convert the hydrogen atoms state equations into cartesian coordinates or should I keep the spherical ones and just convert the electric field? Or is that necessary?

Should I only regard the magnitude of the electric field or is the direction relevant?

I am confused. :S

 

[javierR]

You're perturbing with an interaction of the form $E\cdot \mu$, where $\mu=e*r$ is the dipole moment for the electron relative to the origin of the Hydrogen atom (e is the charge of the electron and r is the vector pointing to the electron). With the electric field E in the +z direction, the dot product gives $|E||r|cos\theta$, where theta is the angle in spherical coordinates with respect to the z-axis, and |r| is the radial distance r in spherical coordinates.

 

[denian]

First of all, it is important to clarify that the use of perturbation theory in this scenario is to determine the probability of finding hydrogen atoms in a certain state in the presence of an electric field. This is a common approach in quantum mechanics when dealing with perturbations in a system.

In order to apply first order perturbation theory, it is not necessary to convert the equations of the hydrogen atom into Cartesian coordinates. The spherical coordinates can still be used, as the perturbation is only applied in the z-direction. However, it is important to consider the effect of the electric field on the Hamiltonian of the system, which will involve converting the electric field into the appropriate units and coordinates.

The direction of the electric field is also relevant, as it will affect the perturbation on the system and therefore the probability of finding the atoms in a certain state. The magnitude of the electric field will also play a role in the calculation, as it will determine the strength of the perturbation.

If you are still confused, I would recommend consulting a textbook or seeking guidance from a mentor or colleague who is familiar with perturbation theory in quantum mechanics. It is a complex topic and it is important to have a solid understanding before attempting any calculations.