Have a question from my class which I'm struggling with.
We have a particle $m$ with wavefunction $φ=Ax \exp(-ax)$ when $x≥0$, and $φ=0$ otherwise.
We are asked to show that the double derivative $φ''=(a²-2a/x)φ.$ So far so good.
Then "Supposing that the particle is an eigenstate of the hamiltonian, determine the potential V(x) and the total energy E of this state.
I've worked through this and got the Schrödinger eq into the form:
After this I'm not sure what to do. How can I separate energy and potential with the information I've been given ?