Yes, because when the annihilation operator works on the state zero, we will get zero by definition according to my book so I thought that there was no point in taking it. But I can see that that would get me on the right track again, but I don't know how I can do it?
But by taking the sum...
Homework Statement
Find the eigenvector of the annhilation operator a.
Homework Equations
a|n\rangle = \sqrt{n}|{n-1}\rangle
The Attempt at a Solution
Try to show this for an arbitrary wavefunction:
|V\rangle = \sum_{n=1}^\infty c_{n}|n\rangle
a|V\rangle = a\sum_{n=1}^\infty c_{n}|n\rangle...