A system can be represented by (H is the Hamiltonian operator).
Show is an eigenfunction of and calculate the eigenvalue. Then, by normalizing, find .
I have the answer, but not sure how they get it. It is:
Eigenvalue = 3
The eigenvalue equation is
So you need to show that
for some constant value of . Really all you are doing here is using the differential operator on the trial wavefunction and solving for .
To get a value for A, then
(You may assume that A is a real number.) This integral is easily done by integration by parts, or using a substitution to rewrite it as a gamma function, or simply looking it up in a table. It's a rather well known integral in Physics.
-Dan