What is difference between ≈ and ~? I'm reading a quantum mechanics book, and it has the following equation:
$$
\Delta x \approx \frac{\lambda}{\sin\alpha} \sim \frac{h}{mc\sin\alpha}
$$
What is the difference between $\approx$ and $\sim$?

$\approx$ is used as the mathematical "approximately" symbol $-$ this means $ \Delta x $ has approximately the same value as $ \frac {\lambda}{\sin \alpha} $. However, $\sim$ is used a proportionality symbol, so there is some factor tacked onto $\frac{h}{mc\sin \alpha}$, which may be $1000$ or $2$ or something else. 
