### Calculate Energy levels of QHO by Finite Difference Method

Differential equations represent a method of understanding how variables change with respect to another variable - position with respect to time, for instance. We use these equations as a mathematical tool to understand the dynamics of a system such as how planetary bodies interact,

### Calculate Determinant by Permutations

While reading through *Modern Quantum Chemistry* by Szabo and Ostlund I came across an equation (1.38) to calculate the determinant of a matrix by permuting the column indices of the matrix elements,

### Plotting Densities with XSF

Suppose you had a wave function or electron density that you need to plot and you want to visualize some molecular or atomic orbital without having to use a fancy (costly) package to do so. This article will go through a little script at how you can go from wave function to electron density using a few freely available tools to produce decent looking figures. The XSF file format is useful to describe 3D data and has been around quite a while so it is compatible with many different visualization packages. Visualization will be done with the VESTA package which excels at plotting 3D scalar fields and crystal structures.

### Interesting Python - Reducing the Elements of a List

During the past week I encountered an interesting problem: If given a list of positive integers, how do you reduce them to become sequential. For example, if you are given the list: