With my exam on Friday, I'm trying to get all these practice probs done since some of them will be on the exam.
If is the Parity Operator, determine the parity of the functions below:
Now, if is the Hamiltonian Operator with , find the parity of
So for the first func, we know that sin(x) is an odd function, and hence that would be -sin(x) if I'm not mistaken since the parity would take sin(x) and make it sin(-x) and thus it'd have parity -1? We only dealt with cos/sin in our notes, so I'm not sure what an extra operator does and the role of exponential functions.
Originally Posted by DiscreteW
The parity operator in 1 - D, as Isomorphism suggests, maps f(x) to f(-x). In 3-D it maps the function f(x, y, z) to f(-x, -y, -z).
Originally Posted by Isomorphism
I think all that is being asked for here is what the parity of the function is. So
, so sin(x) has an odd parity, or -1.
so is not a parity eigenstate.
so has an even parity, or +1.
H is the Hamiltonian operator:
We can do in two ways: Apply H to then apply P, or we can apply P to directly as P is a linear operator. I think at this level it is more instructive to take the former route, so
We know that V(x) has an even parity so this is
so this is not a parity eigenstate.