# Finding a Wave Function

1. Dec 5, 2004

On My Last Straw Trying to Find a Wave Function

I am horribly confused as how to I can actually find a wave function for any given problem. The specific wave function I am trying to find right now is that of a neutron passing through a double slit apparatus. Here is how I have the problem set up thus far:

d= spacing between slits= 1.00 x 10^-3 m (or 1.oo mm)
L= distance between slit apparatus and the detector array = 10.0 m
y= distance on detector array from major maximum (the one in the middle)
m= # of high intensity bands away from middle with the middle one at m=0
v= velocity of the neutron = .400 m/s
w= mass of neutron= 1.67 x 10^-27 kg
h=Planck's constant = 6.63 x 10^-34 Js

I know that the wave function should demonstrate where the destructive interference is going on by being zero when y=(m+.5)(hL/vwd). It should also show the bright spots as maximums and minimums at y=(mhL)/(vwd). I figured that since wave functions are a lot like amplitude functions, this will be a cosine function. My best guess is ... what's that pitchfork sign? ... anyway, that the wave function equals cos(2(pi)ywv/h). Sorry, I don't know how to put a pi in the equation. :uhh:
This cosine function maxes at y=0, which is good; that is what the interference pattern does. But a lot of trig functions could do that, and I cannot justify why mine is a good one. Is it a wave function that describes this neutron? If it is, why? If not, how do I find a function that does?

Last edited: Dec 5, 2004