An atom laser spits out a pulse of atoms that in some ways behaves like light fr
ID: 2124566 • Letter: A
Question
An atom laser spits out a pulse of atoms that in some ways behaves like light from an optical laser, in the sense that it has a well defined wavelength. When running our atom laser in pulsed operation, each atom in the pulse is described by the initial wavefunction
2
?(x,0)=Ae2?2 e , (1)
where k0 and ? are determined by how we pulse our atom laser. Assume that there are no forces acting on our atoms, that is V (x) = 0.
1. (1 mark) Calculate the momentum space wavefunction. What is the expectation value of the momentum? You can calculate it if you want, but it
Explanation / Answer
E=12kx2
KE=12kx2sin2(?ot+?)
PE=12kx2cos2(?ot+?)
Would suggest at
x=0
would have a minimum and where
cos2(?ot+?)=0
would be another minimum.
For a max we have
x=?
with
cos2(?ot+?)=1
.
We are looking for the bounds of the KE. Since 0?sin2??1, the KE is bounded by 0 and E. Now we plug in the E for the ground state of the quantum harmonic oscillator, which is ...?
p=mdxdt
. So I guess I'm not quite sure what you mean. I'm probably just being an idiot here and it should be very simple.
Since KE = p^2/2m, the bounds on KE tell us the bounds on p for the classical oscillator.