How Can Plane Wave Solutions Apply in Charged Particle Interactions?

[ashok vardhan]

Hi all,

While I am reading interaction of atoms with radiation the following doubt came to me...While solving Maxwell equations in a charge and current free region, we get solutions for Vector potential,Electric field and so on which are plane wave solutions...However, when we study the interaction of these fields with say Hydrogen atom/any charged particle, to compute the interaction Hamiltonian we still use the same potential as before...My doubt is that when we placed an charged particle, the space is no more a charge free region..How can we still use the same old solutions of Maxwell equations for potential and carry out the computations..Am I missing any crucial point..?.Please help me in solving this doubt..

 

[eljose79]

Hi there,

This is a great question and one that many scientists have grappled with in the past. The key to understanding this is to remember that the solutions to Maxwell's equations are not affected by the presence of a charged particle. This is because Maxwell's equations describe the behavior of electromagnetic fields, which are not affected by the presence of a single charged particle.

When we study the interaction of these fields with a charged particle, we are looking at the effects of the particle on the fields, not the other way around. This means that we can still use the same solutions for the fields, as they are not affected by the presence of the particle. The only thing that changes is the boundary conditions, as now we have a charged particle in the region.

To compute the interaction Hamiltonian, we use the potential from the solutions to Maxwell's equations, but we also take into account the effects of the charged particle on the fields. This is done through the use of Green's functions, which allow us to calculate the potential at any point in space, taking into account the presence of the charged particle.

I hope this helps to clarify your doubt. Please let me know if you have any further questions.