de Broglie’s Postulates
de Broglie's Postulates
de Broglie postulated that particles of matter have wave nature:
Proposition
The dispersion relation for non-relativistic particle is
Thus the group velocity can be derived:
Free Particle de Broglie Waves
From the standpoint of our quantum mechanics, there is no quantity which causally fixes the effect of a collision in an individual event.
Comment
In Max Born’s statistical interpretation, the state of a particle is represented by a complex function
such that is the probability of finding that particle at the time in the volume element at the point .
e.g. In one dimensional case, we have the probability of finding the particle between
Proposition
The mean position is given by
Momentum Space Wave Function
Given the wave function
, we can use Fourier transform to obtain the wave function in the momentum space: