Schroedinger's Equation for Electromagnetic field induced by charged wire

[opticalnectar]

Greetings all!

I'm completely new to Quantum Mechanics (my PhD research is in Computer Vision) and I am planning to apply some concepts to my research.

I would like to know whether it's possible to get the Wave Equation over the components of a [itex]\mathbf{B}=(B_\phi,B_r,B_z)[/itex] field induced by a straight infinite wire charged with current density [itex]\mathbf{j}[/itex]. I.e [itex]\Psi(B_\phi,B_r, B_z)[/itex]. Basically I want the quantum solution to the classical problem of finding the induced B field by a charged wire of infinite length.

Is this something heard of? If so does anyone have a reference/lead?

I'm assuming QED deals with particles that enter such electromagnetic fields and the wave function is over the postion/impulse of the particles and not the field components at a particular position. Is this correct?

Thanks!

 

[eljose79]

Hello there!

It is definitely possible to use quantum mechanics to study the classical problem of an induced magnetic field from a charged wire. This is known as the Aharonov-Bohm effect, where the wave function of a charged particle is affected by the magnetic field even if it is located in a region where the magnetic field is zero. In this case, the wave function would depend on the components of the magnetic field at a particular position.

There are several papers and books that discuss this effect, including "The Aharonov-Bohm Effect: Variations on a Theme" by Yakir Aharonov and David Bohm, and "Introduction to Quantum Mechanics" by David J. Griffiths. Additionally, there are many research papers on this topic that may be helpful for your specific research interests.

You are correct in your assumption that quantum electrodynamics (QED) deals with particles interacting with electromagnetic fields, and the wave function is typically described in terms of position and momentum of the particles. However, the Aharonov-Bohm effect is an example of how the wave function can also depend on other physical quantities, such as the components of a magnetic field.

I hope this helps guide your research and I wish you the best of luck in applying quantum mechanics to computer vision. It's always exciting to see interdisciplinary applications of science!