# Confusion between the de Broglie wavelength of a particle and wave packets

So I learned that the de Broglie wavelength of a particle, $\lambda = \frac{h}{p}$, where h is Planck's constant and p is the momentum of the particle. I also learned that a quantum mechanics description of a particle is a wave packet. I learned that a wave packet is a summation of different basis functions overlapped over each other at say $x = 0$, and these basis functions are the wave functions, $\Psi(x,t)$. Or is it the probability density, $|\Psi(x,t)|^2$ ??? Please correct me on this.

I learned that the more localized the wave packet is in position space, the more un-localized or uncertain you are about the spread of momentum functions. Please also edit my statement I just said because I don't think I stated it in the best way.

My question is, you have a particle that is represented by a wave packet that is localized, thus, it has a spread of momentum, so how can you then know it's de Broglie wavelength? Do you average together all the different momentum the particle has and then plug that average momentum into $\lambda = \frac{h}{\langle p\rangle}$ ??

• Help me Luboš Motl!!! You know so much!!! – QEntanglement May 19 '11 at 21:50