Frequency Spectrum and Energy of an electromagnetic impulse

The energy associated with an electromagnetic wave, in its simplest form, is given by the relation: $$E = h\nu$$ Where $h$ is Planck's constant. However, this energy relates to a definite frequency. In an electromagnetic impulse, there is a frequency band contained in the wave packet. Does this mean that an impulse also contains a band of energy values? Something along the lines of: $$\Delta E = h\Delta\nu$$ The most intuitive idea of this could be a superposition of (analytically possible, maybe not so physically accurate) photons, each carrying its own energy?

• Granted, I have never thought about that. But what you are saying, makes sense. One should not think of a photon being only a particle or strictly a wave. It is both of them and non of them. You can use a Fourier decomposition to represent an impulse with a great success and not only analytically. It will have its own limited physical sense - wave packet. The word "limited" should not scare you away. Understanding of what photon is is limited in general =) – MsTais Dec 24 '17 at 17:32
• Perhaps helpful: Monochromatic pulses – HolgerFiedler Dec 25 '17 at 10:37
• @MsTais Yes, I only refer to "photon" as a synonym for "electromagnetic wave". They are two aspects of the universe we read in different situations, both produced by the same nature; as much as energy density and pressure are. – Niki Di Giano Dec 25 '17 at 11:13