I'm doing some past papers for my QM finals and I've come across a question that is a bit strange. I'm not sure if it's as easy as it sounds.
X and P are one dimensional position and momentum operators, which take the explicit forms of x and -ihd/dx.
i) write down the explicit forms of X^2 and P^2
now then, is this just x^2 and hd^2/dx^2?
im ok on the next few bits, but:
iv) which, if any, of the two functions exp(ikx) and exp(-ax^2) are eigenfunctions of P^2?
my guess is that, since the eigenfunction of P is exp(ikx), its the other one (and the i has disapeared in the squaring process), but how can i prove this?
Im probably just being paranoid, but can someone verify these answers?