I How to quantum mechanically describe the photon?

[Somali_Physicist]

This might sound stupid , but I am wondering how exactly could I describe the momentum eigenfunctions of photons?

EDIT:
to destroy ambiguity, I am searching for a quantum mechanic description of monochromatic light similar to how we represent it classically as:

E^-> = a^->cos(wt+phi)

 

[Demystifier]

This might sound stupid , but I am wondering how exactly could I describe the momentum eigenfunctions of photons?

$|p>$

 

[A. Neumaier]

$|p>$

more precisely, $|p\rangle$

 

[BvU]

witty responses and as true as true can be. does it help our @Somali_Physicist ?

 

[Avodyne]

A quantum description of photons requires quantizing the electromagnetic field. This is discussed in any textbook on quantum field theory or quantum optics, and in many quantum-mechanics textbooks. This will result in operators that create and destroy photons with definite momentum and polarization. Acting on the vacuum (the state of no particles) with a single-photon creation operator produces a momentum eigenfunction. Acting with the exponential of a creation operator (with a specific coefficient) will create a "coherent state" of photons, all with the same momentum, which is as close as you can get to a classical field in the quantum theory.

 

[Somali_Physicist]

A quantum description of photons requires quantizing the electromagnetic field. This is discussed in any textbook on quantum field theory or quantum optics, and in many quantum-mechanics textbooks. This will result in operators that create and destroy photons with definite momentum and polarization. Acting on the vacuum (the state of no particles) with a single-photon creation operator produces a momentum eigenfunction. Acting with the exponential of a creation operator (with a specific coefficient) will create a "coherent state" of photons, all with the same momentum, which is as close as you can get to a classical field in the quantum theory.

Thank you
So there is no one liner equation ?

What is your textbook called

 

[Avodyne]

You could try David Tong's lecture notes:
http://www.damtp.cam.ac.uk/user/tong/qft/qft.pdf

 

[DarMM]

This might sound stupid , but I am wondering how exactly could I describe the momentum eigenfunctions of photons?

Weinberg's "The Quantum Theory of Fields" Chapter 2 has a nice discussion of momentum eigenstates of various particle types.

$|p>$

more precisely, $|p\rangle$

There should also be helicity right? $|p,\sigma\rangle$

 

[A. Neumaier]

There should also be helicity right? $|p,\sigma\rangle$

Or helicity left, $|p, - \sigma\rangle$

 

[A. Neumaier]

So there is no one liner equation

The relevant equation is that for the vector potential of the e/m field in Lorentz gauge.

 

[Demystifier]

Or helicity left, $|p, - \sigma\rangle$

What's the difference between the left and and right side of the brain? On the right side there is nothing right, while on the left side there is nothing left.

 

[Pony]

On the right side there is nothing right, while on the left side there is nothing left.

I prefer this: On the left side there is nothing right, while on the right side there is nothing left.

 

[Demystifier]

I prefer this: On the left side there is nothing right, while on the right side there is nothing left.

It's not sufficiently paradoxical. A quantum description is not good if it does not look like a paradox.

 

[vanhees71]

It's not even right since on the right hand the thumb is at the left...

 

[bhobba]

What is your textbook called

I would start with the following:
http://www.physics.usu.edu/torre/3700_Spring_2015/What_is_a_photon.pdf

Thanks
Bill