How to Derive the Wave Equations for Photons?

[jb646]

Homework Statement

Use the relativistic expression for energy E^2=p^2c^2+(m_0)^2(c)^4 to find a wave equations for photons. Find a solution for ψ and compare to the electric field (hint: photons are massless, E_op=ih(d/dt) and p_op=h/i(d/dx)

Homework Equations

the only equations i know are the ones given in the problem

The Attempt at a Solution

if somebody could please point me in the right direction, i do not have the mental power to understand what i should even try to do first. Thanks for any help you can provide.

 

[dextercioby]

Photons are quanta of fields, it doesn't really work the way your problem suggests.

The differential equation for the quantized electromagnetic field is obtained by applying a canonical quantization* to the classical electrodynamic equation for the one-forms describing the field at a classical level.

* very tricky issue.

 

[Redbelly98]

Homework Statement

Use the relativistic expression for energy E^2=p^2c^2+(m_0)^2(c)^4 to find a wave equations for photons. Find a solution for ψ and compare to the electric field (hint: photons are massless, E_op=ih(d/dt) and p_op=h/i(d/dx)

Homework Equations

the only equations i know are the ones given in the problem

The Attempt at a Solution

if somebody could please point me in the right direction, i do not have the mental power to understand what i should even try to do first. Thanks for any help you can provide.

Okay, if E_op=ih(d/dt), then what would E_op² be?

Photons are quanta of fields, it doesn't really work the way your problem suggests.

The differential equation for the quantized electromagnetic field is obtained by applying a canonical quantization* to the classical electrodynamic equation for the one-forms describing the field at a classical level.

* very tricky issue.

I fail to see how that is helpful.

 

[dextercioby]

I fail to see how that is helpful.

The problem is wrong. The photon has no wave equation. The electric field has a field equation, but in the classical sense, as it can be deduced from Maxwell's equations (for simplicity, in vacuum).