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I'm trying to learn some basic quantum mechanics and I have a question related to group velocity of a travelling wave. I know there are already a few questions related to group velocity, but I couldn't find any answers that address mine.

So, I understand that group velocity is the velocity of the wave 'envelope' (i.e. outline shape) of a collection of superimposed travelling waves. However, is it the case that, for any arbitrary collection of such travelling waves, there will always be a wave envelope that retains the same shape as the collection of waves propagate? Or, will that happen only in certain situations, or for certain combinations of waves? Will any arbitrary collection of waves have a group velocity?

Qmechanic
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Time4Tea
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For any arbitrary collection of such travelling waves will always be a wave envelope that retains the same shape as the collection of waves propagate?
No, it will not. For example, a Gaussian wave-packet will spread out in time. Wave packets are used to represent localization of particles in Quantum Mechanics.Group velocity will give the physical velocity of the particle. For example, a moving electron can be represented by a wave-packet whose group velocity will give the velocity of the particle.

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