- #1
Zarlucicil
- 13
- 2
I'm in the process of doing a quantum physics lab and am having a bit of trouble with uncertainty. The specific things going on in the lab aren't relevant, I don't think, only the general procedure of my calculation. Also, I'm not certain where this question should be asked, so I decided to put it here (General Physics).
Let's say we are measuring a quantity x that has an uncertainty of b. Thus,
[tex] x \pm b [/tex].
Clearly, x has a maximum and minimum value. Namely,
[tex] x_L = x - b [/tex]
[tex] x_H = x + b [/tex].
There is another quantity y, which is constant, that has an uncertainty of d. It appears y also has a maximum and minimum value,
[tex] y_L = y - d [/tex]
[tex] y_H = y + d [/tex].
Now we want to multiply these two quantities together to get a new quantity z = xy. It seems that this value z has a maximum and minimum value as well,
[tex] z_L = y_L x_L [/tex]
[tex] z_H = y_H x_H [/tex].
Is it permissible to say that the uncertainty on z is the following? (The length between the two extreme values of z divided by 2)
[tex] \frac{z_H - z_L}{2} [/tex].
So, after we measure x we need to multiply by y to get z, and y is a constant which only needs to be measured once, but still as an uncertainty. Can we describe z in the following manner?
[tex] z \pm \left( \frac{z_H - z_L}{2} \right) [/tex]
Let's say we are measuring a quantity x that has an uncertainty of b. Thus,
[tex] x \pm b [/tex].
Clearly, x has a maximum and minimum value. Namely,
[tex] x_L = x - b [/tex]
[tex] x_H = x + b [/tex].
There is another quantity y, which is constant, that has an uncertainty of d. It appears y also has a maximum and minimum value,
[tex] y_L = y - d [/tex]
[tex] y_H = y + d [/tex].
Now we want to multiply these two quantities together to get a new quantity z = xy. It seems that this value z has a maximum and minimum value as well,
[tex] z_L = y_L x_L [/tex]
[tex] z_H = y_H x_H [/tex].
Is it permissible to say that the uncertainty on z is the following? (The length between the two extreme values of z divided by 2)
[tex] \frac{z_H - z_L}{2} [/tex].
So, after we measure x we need to multiply by y to get z, and y is a constant which only needs to be measured once, but still as an uncertainty. Can we describe z in the following manner?
[tex] z \pm \left( \frac{z_H - z_L}{2} \right) [/tex]