Wave packet conceptual question

[musashi1029]

Hello.

I am reading about the wave packet in my physics textbook, and I understood that it describes the probability of a particle having a given position and a momentum in a particular state.
However, I just cannot understand where those waves that consist the wave packet come from. I will be happy if anyone can provide an answer to this question.

Thank you in advance.

 

[atyy]

Like the classical particle, the wavefunction that is a quantum particle comes from nowhere, and is simply assumed to exist. The difference between a classical and a quantum particle is that the former has definite position and momentum.

A momentum measurement corresponds to a momentum operator, which has eigenvalues and eigenfunctions. The wavefunction can be thought to be "made up" of momentum eigenfunctions, just as any sound thought to be "made up" of pure tones. But just as you could use also use spherical harmonics to represent sound, and you can use other basis functions to represent a wavefunction.

 

[musashi1029]

>atyy
The example of sound helped a lot! Thank you!

 

[jtbell]

To carry the sound example further, an example of a wave packet of sound is a single pulse of sound which you can produce by clapping your hands once. It can be analyzed as a sum of pure tones (waves) by using Fourier analysis. This isn't merely a mathematical trick. Those pure tones are affected differently when they pass through a medium (dispersion), and this affects the way the pulse propagates. However, I don't think you can really say where each individual wave "comes from," physically, in terms of the clap that produces the pulse.