- #1

Silversonic

- 130

- 1

## Homework Statement

Show that ψ(x) = Acos(kx) is not an eigenfunction of the momentum operator. If you were to measure the momentum of a particle with this wavefunction, what possible values would you get and what would the probability be of obtaining these values?

## Homework Equations

Momentum operator is;

[itex] -i\frac {h}{2\pi} \frac {d}{dx} [/itex]

## The Attempt at a Solution

It's obvious that it's not an eigenfunction of the operator, but how do I do the latter two questions? If it's not an eigenfunction, how could it be known? I could use the expectation value formula (<p> = ∫ψ*pψdx) but what would my integral values be? Could someone give me a hint?

Someone told me elsewhere that I want the wave function expressed in the momentum representation which is obtained by taking the Fourier transform. Whether that's right or not, this is just meant to be a series of revision questions from my last year quantum mechanics, and we never dealt with Fourier transforms.