The Ladder Operators

a and a^† are known as ladder operators. They occur in the quantum mechanical harmonic oscillator, where they serve the purpose of lowering and raising the states they are acting on, respectively. So for example, if I have state n, acting a on it lowers it to state (n - 1), and acting a^† on it raises it to state (n + 1).

From a philosophical viewpoint, there are two ways to look at the QM2 test tomorrow. One is to see my marks starting at 0, and then having a^† acting on it everytime I do a question correctly. The other is to see it as a full 100 marks, then having a acting on it with every part I leave blank or did wrongly.