Maxwell equations in quantum mechanics

[pankajmaurya]

Maxwell equations are based on the wave nature of electromagnetism so they can't explain why the electron revolving in Bohr's orbit does not emit radiations.So my question is can't the Maxwell equations be modified according to the particle nature(quanta) of electromagnetism

 

[BruceW]

I think this has already happened. Maxwell's equations have been quantised to explain quantum phenomena correctly. (But of course they are no longer of the simple form they were before). I guess you could say that Maxwell's equations gave a clue as to how the quantum world should work. (Similarly to how classical mechanics gave clues as to how the quantum theory should work).
But I don't really know any specifics on the quantisation of the electromagnetic field

 

[jtbell]

I think this has already happened. Maxwell's equations have been quantised to explain quantum phenomena correctly.

And we call this "quantum electrodynamics" (QED). It has been tested against experiment many many times, with great success.

 

[PhilDSP]

Maxwell equations are based on the wave nature of electromagnetism so they can't explain why the electron revolving in Bohr's orbit does not emit radiations.So my question is can't the Maxwell equations be modified according to the particle nature(quanta) of electromagnetism

The Maxwell equations are already able to model particles such as the hydrogen atom in a way that can explain why it doesn't radiate when the orbital is stable. Studies by H. A. Haus, T. A. Abbott, D. J. Griffiths, G. H. Goedecke and P. Pearle clearly show this to be the case.

The difficulty is coming up with a charge model along with a systematic motion that meets all other experimental and theoretical observations. It's not a simple problem.

 

[jfy4]

This web page is a good start:

http://en.wikipedia.org/wiki/Quantum_electrodynamics"

 

[sriecewit]

This web page is a good start:

http://en.wikipedia.org/wiki/Quantum_electrodynamics"

Hi Judah,

Thanks for the quick start link on QED.
But is there any way I can understand the mathematics of QED (starting from the basic model of an atom). I'm interested in learning the theory and my math is just at the undergrad level.

-
Srini

 

[jfy4]

Hi Judah,

Thanks for the quick start link on QED.
But is there any way I can understand the mathematics of QED (starting from the basic model of an atom). I'm interested in learning the theory and my math is just at the undergrad level.

-
Srini

What level of undergrad? Have you taken linear algebra? All 3 calculus courses? Mechanics I and II? if you have, the main item left is tensor calculus, which is, in general, a straightforward generalization of 3-vectors and matrices; although the physical idea behind using tensors and differential forms is much deeper than I perhaps put on...

The mathematics of QFT relies heavily on linear algebra. If you are familiar with it, things should fall into place over time. Although, like I said, drawing physics and identifying physics from the mathematical framework is not trivial, there are hundreds of threads on this website to testify...

 

[sriecewit]

What level of undergrad? Have you taken linear algebra? All 3 calculus courses? Mechanics I and II? if you have, the main item left is tensor calculus, which is, in general, a straightforward generalization of 3-vectors and matrices; although the physical idea behind using tensors and differential forms is much deeper than I perhaps put on...

The mathematics of QFT relies heavily on linear algebra. If you are familiar with it, things should fall into place over time. Although, like I said, drawing physics and identifying physics from the mathematical framework is not trivial, there are hundreds of threads on this website to testify...

Except linear I have taken other courses you have mentioned. Maybe I will study linear algebra and then start with mathematics of QFT. Is that a good idea?

-
Srini