Don't understand transformation (physics problem, but it's about basic math)?
Hey, I somehow don't understand the transformation in the solution. How do you get 1+delta m/m=1+delta n/n? I'm too stupid to use simple fraction arithmetic, so if someone could explain this to me as simply as possible, I'd be super grateful. And why can 1/2 be ignored for n >> 1? Here's the problem, for those who need context (e)
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Actually, it's just multiplication and shorts. But here's a little detailed…
Left side of the equation:
At the right side, this is done exactly.
shortening away can be a first step. This cuts the thing off.
(m + Δm)*gz/(m*gz) = (m + Δm)/m = 1 + Δm/m
On the right side:
(n + Δn + 1⁄2)*ωħ / ((n+1⁄2)*ωħ)
= (n + Δn + 1⁄2) / (n + 1⁄2)
= 1 + Δn / (n + 1⁄2)
1 + Δn/n for n ′′,
because n+1⁄2=n*(1+1/(2*n))) is then n*1=n, because of 1/(2*n)=0.