Source: cirosantilli/ladder-operator
= Ladder operator
{wiki}
http://www.physics.udel.edu/~jim/PHYS424_17F/Class%20Notes/Class_5.pdf by James MacDonald shows it well.
The operators are a natural guess on the lines of "if p and x were integers".
And then we can prove the ladder properties easily.
The <commutator> appear in the middle of this analysis.