I need to choose a GIS system for a small university research centre. We are handling a broad range of data, (for example, numerical tidal analyses, weather data, poverty, isolated economic activity, skills availability and renewable energy resource availability) and operate primarily in countries with relatively poor existing data sets. 

We interact with other groups, some of which use ARCGIS. Do I have to wade through every GIS software descriptor on the web, or can someone please give an indication of likely candidates? 


Question: Zero point fluctuation of an harmonic oscillator
Answer: You can find the value of zero point fluctuations just by calculating the variance $\langle(\Delta\hat{x})^2\rangle = \langle\hat{x}^2\rangle$ in the vacuum state. You can do this either using the $x$-representation or expressing the $\hat{x}$ operator using creation and annihilation operators. These are usually introduced by
$$
\hat{a} = \sqrt{\frac{m\Omega}{2\hbar}}\left(\hat{x}+i\frac{\hat{p}}{m\Omega}\right),
$$
so that you get
$$
\hat{x} = \sqrt{\frac{\hbar}{2m\Omega}}(\hat{a}+\hat{a}^\dagger).
$$
Using this to calculate $\langle\hat{x}^2\rangle = \langle 0|\hat{x}^2|0\rangle$ indeed gives you $$x_{ZPF} = \sqrt{\langle\hat{x}^2\rangle} = \sqrt{\frac{\hbar}{2m\Omega}}.$$