Photon as a wave packet

When electromagnetic waves of different frequencies interact, they give rise to secondary wave structures called envelopes in which individual waveforms form at the rear and die out at the front. These envelopes are called groups and they travel with a velocity called group velocity and the individuals, phases and they travel with a phase velocity. These groups or envelopes are called photons right?
If so, can a photon of monochromatic EM wave exist? I recently studied that the wave function of a particle is the integral over a range of frequencies. This doesn't make sense because while studying the photo electric effect, we assume photons to be monochromatic.