- #1
diracdelta
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Homework Statement
After turnig of magnetic-optic pit, cold cloud of atom 87 Rb is expanding. Size of cloud after time t, is given with relation:
where, k_B is Boltzman constant, m mass of 87 Rb.
Draw a plot, then use least squares method to find temperature T, and initial size of cloud sigma_0, for next results of measurement.
t(ms)
sigma(mm)
The Attempt at a Solution
I am familiar with least squares method. What I don't understand in this problem is next.
First of i must get this formulae to some linear shape ( regrression).
So, ok, firstly we square the whole equation.
I get next.
now, on to assigning values to get form like y=ax+b, its obvius,
y= sigma^2
b=sigma_0^2
x=t^2
x= (k_B * T)/m
and now, to use least square methd, i must calculate, x,y,xy,x^2,y^2, and sum of them all.
my question here is next:
This member boltzman constant/m. What should i do with it?
Shuld i calculate it and continue to multiply numbers with it whole process?
Or just write results like 0.157746 * ( K-b/m) and in the end multiply a with it?