- #1

- 10

- 0

## Homework Statement

I doubt that my problem is supposed to be in the Advanced Physics forum, but the subject is advanced. Okay, my problem is pretty stupid. The assignment is deriving a probability using some approximations and such, for 2-neutrino oscillation. I can do the entire calculation (which isn't difficult), except for one thing and that is the unit conversion

The problem statement is rewriting the left hand side to the right hand:

[tex]\frac{\Delta m^2 c^3 L}{4 \hbar E} \cong 1.27\frac{ \Delta m^2 L}{E}[/tex]

, with m in [tex]\mathrm{eV} / c^2[/tex], E in [tex]\mathrm{GeV}[/tex] and L in [tex]\mathrm{km}[/tex]

## Homework Equations

[tex]\frac{\Delta m^2 c^3 L}{4 \hbar E} \cong 1.27\frac{ \Delta m^2 L}{E}[/tex]

## The Attempt at a Solution

So okay, I assume the terms on the left hand side are in SI units. So mass can be expressed as J / c^2. One eV is equal to the e*J with e the charge of the electron. J is therefor equal to the reciprocal of e multiplied with eV. Insert that into the term and I thought I had converted J successfully to eV with factor of 1/e. But here is the problem, this becomes approximately 10E19 squared, and dividing it to Planck's constant, gives an enormous factor, inconsistent with the answer.

Now I know this problem is stupid, but my brain is not cooperating. I know what to do to get the factor 1.27, but I don't understand why! You can get the 1.27 factor, simply by replacing the units with the new units and calculating that:

[tex]\frac{(1.6*10^{-19})^2 10^3}{4\hbar 10^9 1.6*10^{-19} c} \cong 1.2669[/tex]

I find the use of units and conversions in HEP in general rather confusing.