Natural Science Forum / Physics / Research / September 2004

The general wavefunction for a free particle is:

Y (x,t) = A cos( kx - wt) + iA sin (kx - wt)

and the complex conjugate is:

Y*(x,t) = A cos( kx - wt) - iA sin (kx - wt)

These are multiplied together to give,along with a proportionality
constant,
the probability of finding a particle at a particular place at a
particular time.It is not known why this should be so.Here is a
suggestion:

If the wavefunction already represents a probability before it is
squared,
then multiplying it by another wavefunction  - the complex conjugate -
suggests that we are dealing with the probability of two events
occurring simultaneously.This could be the probability of a mass being
in a particular place at a particular time, and something that is
equivalent to the mass being at that place at the same time.Writing
new wavefunctions Y1 and Y2:

Y1 = A cos (kx - wt), Y2 = iA sin (kx -wt)

then Y = Y1 + Y2

and Y* = Y1 - Y2

This is the kind of relation between wavefunctions that one gets
for a hydrogen molecule, for example.
Does anyone agree that the product YY* could be
telling us about two different particles in the same place at the same
time?