# Photon's multiple frequencies by Fourier

Since any source of light will have a finite duration, the light emited won't have a particular frecuency. It will be a sum of different frequencies (infinite, I think) if we apply Fourier's series (integral).

Would this mean that any photon's frequency will have some uncertainty or something like the photon emitted would be a combination of different photons?

$\Delta\omega\Delta t \geq \frac{1}{2}$.
• Is this a good interpretation of the energy-time uncertainty? I only know that $\Delta t$ refers to the evolution of the Hamiltonian. – jinawee Jun 22 '13 at 19:31
• This mechanism is, in fact, how very short particle lifetimes are measured. You find the width of the line in energy space and apply the HUP in it $\Delta E \Delta t$ form. – dmckee --- ex-moderator kitten Jun 22 '13 at 19:38
• The $\Delta t$ refers to the amount of time it takes for the expectationvalue of an observable to change by one standarddeviation. So it depends on what observable you are looking at, which in your case probably is the amplitude of the light in a given range of frequencies. – Nick Jun 22 '13 at 19:46